!
!////////////////////////////////////////////////////////////////////////
!
!
! Manufactured solutions definitions for 2D and 3D cases (Euler and Navier-Stokes)
!
!
!////////////////////////////////////////////////////////////////////////////////////////
MODULE ManufacturedSolutionsNS
USE SMConstants
USE PhysicsStorage_NS
USE Physics_NS
use FluidData_NS
IMPLICIT NONE
private
public InitializeManufacturedSol, ManufacturedSolP
public ManufacturedSolutionState, ManufacturedSolutionDeriv
public ManufacturedSolutionSourceEuler
public ManufacturedSolutionSourceNS
REAL(KIND=RP), DIMENSION(7) :: rC, uC, vC, wC, pC
!========
CONTAINS
!========
!
!///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
!
SUBROUTINE InitializeManufacturedSol(ProblemDIM)
IMPLICIT NONE
!
! --------------------------------------------------------------------------------------
! Constant definitions for the manufactured solutions.
!
! The primitive variable j(rho, u, v, w, p) is defined as:
! j = jC(1) + jC(2)*Sin(pi*jC(5)*x) + jC(3)*Sin(pi*jC(6)*y) + jC(4)*Sin(pi*jC(7)*z)
! See:
! |> Roy, Chris, Curt Ober, and Tom Smith. "Verification of a compressible CFD code
! using the method of manufactured solutions." 32nd AIAA Fluid Dynamics Conference
! and Exhibit. 2002.
! --------------------------------------------------------------------------------------
!
CHARACTER(LEN=*) :: ProblemDIM
SELECT CASE (ProblemDIM)
CASE ('2D')
!
! -------
! 2D case
! -------
!
rC = (/1._RP, 0.15_RP ,-0.1_RP , 0._RP, 1._RP , 0.50_RP , 0._RP/)
uC = (/1._RP, 0.0625_RP ,-0.0375_RP , 0._RP, 1.5_RP , 0.60_RP , 0._RP/)
vC = (/1._RP,-0.09375_RP , 0.05_RP , 0._RP, 0.5_RP , 2._RP/3._RP, 0._RP/)
wC = (/0._RP, 0._RP , 0._RP , 0._RP, 0._RP , 0.00_RP , 0._RP/)
pC = (/1._RP, 0.2_RP , 0.5_RP , 0._RP, 2.0_RP , 1.00_RP , 0._RP/)
CASE ('3D')
!
! -------
! 3D case
! -------
!
rC = (/1._RP, 0.15_RP ,-0.10000_RP ,-0.12000_RP, 1.0_RP , 0.50_RP , 1.50_RP/)
uC = (/1._RP, 0.0625_RP ,-0.03750_RP ,-0.02250_RP, 1.5_RP , 0.60_RP , 0.50_RP/)
vC = (/1._RP,-0.09375_RP , 0.05000_RP , 0.03750_RP, 0.5_RP , 2._RP/3._RP, 1.25_RP/)
wC = (/1._RP, 0.01875_RP ,-0.03125_RP , 0.04375_RP, 1.0_RP/3._RP, 1._RP/5._RP, 1.00_RP/)
pC = (/1._RP, 0.2_RP , 0.50000_RP ,-0.35000_RP, 2.0_RP , 1.00_RP , 1._RP/3._RP/)
!~ rC = (/1._RP,-0.15_RP ,-0.15000_RP ,-0.15000_RP, 5.0_RP , 5.0_RP , 5.00_RP/)
!~ uC = (/0._RP, 0.5_RP , 0.5_RP , 0.5_RP , 1.0_RP , 1.00_RP , 1.00_RP/)
!~ vC = (/1._RP,-0.09375_RP , 0.05000_RP , 0.03750_RP, 0.5_RP , 2._RP/3._RP, 1.25_RP/)
!~ wC = (/1._RP, 0.01875_RP ,-0.03125_RP , 0.04375_RP, 1.0_RP/3._RP, 1._RP/5._RP, 1.00_RP/)
!~ pC = (/1._RP, 0.2_RP , 0.50000_RP ,-0.35000_RP, 2.0_RP , 1.00_RP , 1._RP/3._RP/)
END SELECT
END SUBROUTINE InitializeManufacturedSol
!
!///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
!
FUNCTION ManufacturedSolP(x) RESULT(p)
IMPLICIT NONE
REAL(KIND=RP) :: x(3), p
p = pC(1) + pC(2)*Sin(pi*pC(5)*x(1)) + pC(3)*Sin(pi*pC(6)*x(2)) + pC(4)*Sin(pi*pC(7)*x(3))
END FUNCTION ManufacturedSolP
!
!///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
!
SUBROUTINE ManufacturedSolutionState( x, t, Q )
IMPLICIT NONE
!
! ----------------------------------------------------
! Manufactured solution state (valid for Euler and NS)
! ----------------------------------------------------
!
REAL(KIND=RP) :: x(3), t
REAL(KIND=RP) :: Q(NCONS)
REAL(KIND=RP) :: rho, u, v, w, p
associate ( gamma => thermodynamics % gamma )
rho = rC(1) + rC(2)*Sin(pi*rC(5)*x(1)) + rC(3)*Sin(pi*rC(6)*x(2)) + rC(4)*Sin(pi*rC(7)*x(3))
u = uC(1) + uC(2)*Sin(pi*uC(5)*x(1)) + uC(3)*Sin(pi*uC(6)*x(2)) + uC(4)*Sin(pi*uC(7)*x(3))
v = vC(1) + vC(2)*Sin(pi*vC(5)*x(1)) + vC(3)*Sin(pi*vC(6)*x(2)) + vC(4)*Sin(pi*vC(7)*x(3))
w = wC(1) + wC(2)*Sin(pi*wC(5)*x(1)) + wC(3)*Sin(pi*wC(6)*x(2)) + wC(4)*Sin(pi*wC(7)*x(3))
p = pC(1) + pC(2)*Sin(pi*pC(5)*x(1)) + pC(3)*Sin(pi*pC(6)*x(2)) + pC(4)*Sin(pi*pC(7)*x(3))
Q(1) = rho
Q(2) = rho*u
Q(3) = rho*v
Q(4) = rho*w
Q(5) = p/(gamma - 1.0_RP) + 0.5_RP*rho*(u**2 + v**2 + w**2)
end associate
END SUBROUTINE ManufacturedSolutionState
!
!///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
!
SUBROUTINE ManufacturedSolutionDeriv( xx, t, nHat, U_x, U_y, U_z )
!
! ------------------------------------------------------
! Manufactured solution derivatives (only needed for NS)
! ------------------------------------------------------
!
IMPLICIT NONE
REAL(KIND=RP) :: xx(3), t
REAL(KIND=RP) :: nHat(3)
REAL(KIND=RP), INTENT(INOUT) :: U_x(NGRAD), U_y(NGRAD), U_z(NGRAD)
REAL(KIND=RP) :: x, y, z
associate ( gammaM2 => dimensionless % gammaM2 )
x = xx(1)
y = xx(2)
z = xx(3)
! u (velocity)
U_x(1) = pi*Cos(pi*x*uC(5))*uC(2)*uC(5)
U_y(1) = pi*Cos(pi*y*uC(6))*uC(3)*uC(6)
U_z(1) = pi*Cos(pi*z*uC(7))*uC(4)*uC(7)
! v (velocity)
U_x(2) = pi*Cos(pi*x*vC(5))*vC(2)*vC(5)
U_y(2) = pi*Cos(pi*y*vC(6))*vC(3)*vC(6)
U_z(2) = pi*Cos(pi*z*vC(7))*vC(4)*vC(7)
! w (velocity)
U_x(3) = pi*Cos(pi*x*wC(5))*wC(2)*wC(5)
U_y(3) = pi*Cos(pi*y*wC(6))*wC(3)*wC(6)
U_z(3) = pi*Cos(pi*z*wC(7))*wC(4)*wC(7)
! T (Temperature)
U_x(4) = -((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + rC(4)*Sin(pi*z*rC(7)))
U_y(4) = -((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + rC(4)*Sin(pi*z*rC(7)))
U_z(4) = -((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + rC(4)*Sin(pi*z*rC(7)))
end associate
END SUBROUTINE ManufacturedSolutionDeriv
!
!///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
!
SUBROUTINE ManufacturedSolutionSourceNS( xx, t, Q )
!
! --------------------------------
! Source term for MS Navier Stokes
! --------------------------------
!
IMPLICIT NONE
REAL(KIND=RP) :: xx(3), t
REAL(KIND=RP) :: Q(NCONS)
REAL(KIND=RP) :: x, y, z
associate ( gamma => thermodynamics % gamma, &
Mach => dimensionless % Mach, &
Re => dimensionless % Re, &
Pr => dimensionless % Pr, &
gammaM2 => dimensionless % gammaM2 )
x = xx(1)
y = xx(2)
z = xx(3)
!
! -------------------------
! Mass equation Source term
! -------------------------
!
Q(1) = Q(1) + pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4)) &
+ pi*Cos(pi*x*uC(5))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*uC(2)*uC(5) + &
pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4)) &
+ pi*Cos(pi*y*vC(6))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*vC(3)*vC(6) + &
pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*z*wC(7))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*wC(4)*wC(7)
!
! -------------------------------
! x-momentum equation Source term
! -------------------------------
!
Q(2) = Q(2) + pi*Cos(pi*x*pC(5))*pC(2)*pC(5) + &
pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))**2 + &
2*pi*Cos(pi*x*uC(5))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*uC(2)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4))* &
uC(5) + pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4))* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4)) &
+ pi*Cos(pi*y*uC(6))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*uC(3)*uC(6)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4)) &
+ pi*Cos(pi*y*vC(6))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*(uC(1) + Sin(pi*x*uC(5))*uC(2) + &
Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4))*vC(3)*vC(6) + &
pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4))* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*z*uC(7))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*uC(4)*uC(7)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*z*wC(7))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*(uC(1) + Sin(pi*x*uC(5))*uC(2) + &
Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4))*wC(4)*wC(7) - &
((-2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*uC(5))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*uC(2)*uC(5))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(2*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)*Cos(pi*x*rC(5))*Cos(pi*x*uC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*uC(2)*uC(5))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(2*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)*Cos(pi*x*pC(5))*Cos(pi*x*uC(5))*pC(2)*pC(5)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*uC(2)*uC(5))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*uC(5))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*uC(2)*uC(5))/ &
(Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(4*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*x*uC(5))*uC(2)*uC(5)**2)/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*y*uC(6))*uC(3)*uC(6)**2)/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*z*uC(7))*uC(4)*uC(7)**2)/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*pC(6))*pC(3)*pC(6)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
(2.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*pC(7))*pC(4)*pC(7)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
(2.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(2*gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) + &
(2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*pC(5))*pC(2)*pC(5)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))))/Re
!
! -------------------------------
! y-momentum equation Source term
! -------------------------------
!
Q(3) = Q(3) + pi*Cos(pi*y*pC(6))*pC(3)*pC(6) + &
pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4))* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4)) &
+ pi*Cos(pi*x*uC(5))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*uC(2)*uC(5)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4)) &
+ pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))**2 + &
pi*Cos(pi*x*vC(5))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*(uC(1) + Sin(pi*x*uC(5))*uC(2) + &
Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4))*vC(2)*vC(5) + &
2*pi*Cos(pi*y*vC(6))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*vC(3)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4))* &
vC(6) + pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4))* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*z*vC(7))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*vC(4)*vC(7)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*z*wC(7))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*(vC(1) + Sin(pi*x*vC(5))*vC(2) + &
Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4))*wC(4)*wC(7) - &
(-((gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*x*vC(5))*vC(2)*vC(5)**2)/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*pC(5))*pC(2)*pC(5)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
(2.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*vC(6))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*vC(3)*vC(6))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(2*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)*Cos(pi*y*rC(6))*Cos(pi*y*vC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*vC(3)*vC(6))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(2*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)*Cos(pi*y*pC(6))*Cos(pi*y*vC(6))*pC(3)*pC(6)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*vC(3)*vC(6))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*vC(6))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*vC(3)*vC(6))/ &
(Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(4*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*y*vC(6))*vC(3)*vC(6)**2)/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*z*vC(7))*vC(4)*vC(7)**2)/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*pC(7))*pC(4)*pC(7)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
(2.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(2*gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) + &
(2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*pC(6))*pC(3)*pC(6)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))))/Re
!
! -------------------------------
! z-momentum equation Source term
! (2D case!)
! -------------------------------
!
Q(4) = Q(4) + pi*Cos(pi*z*pC(7))*pC(4)*pC(7) + &
pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4))* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*x*uC(5))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*uC(2)*uC(5)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4))* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*y*vC(6))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*vC(3)*vC(6)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))**2 + &
pi*Cos(pi*x*wC(5))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*(uC(1) + Sin(pi*x*uC(5))*uC(2) + &
Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4))*wC(2)*wC(5) + &
pi*Cos(pi*y*wC(6))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*(vC(1) + Sin(pi*x*vC(5))*vC(2) + &
Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4))*wC(3)*wC(6) + &
2*pi*Cos(pi*z*wC(7))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*wC(4)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4))* &
wC(7) - (-((gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*x*wC(5))*wC(2)*wC(5)**2)/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*pC(5))*pC(2)*pC(5)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
(2.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*y*wC(6))*wC(3)*wC(6)**2)/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*pC(6))*pC(3)*pC(6)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
(2.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*wC(7))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*wC(4)*wC(7))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(2*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)*Cos(pi*z*rC(7))*Cos(pi*z*wC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*wC(4)*wC(7))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(2*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)*Cos(pi*z*pC(7))*Cos(pi*z*wC(7))*pC(4)*pC(7)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*wC(4)*wC(7))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*wC(7))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*wC(4)*wC(7))/ &
(Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(4*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*z*wC(7))*wC(4)*wC(7)**2)/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(2*gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) + &
(2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*pC(7))*pC(4)*pC(7)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))))/Re
!
! ---------------------------
! Energy equation Source term
! ---------------------------
!
Q(5) = Q(5) -((-((gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2)/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2)) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2)/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2)/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*pC(5))*pC(2)*pC(5)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2)/ &
(2.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*pC(6))*pC(3)*pC(6)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2)/ &
(2.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*pC(7))*pC(4)*pC(7)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2)/ &
(2.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
((2*gammaM2*pi**2*Cos(pi*x*rC(5))**2*rC(2)**2*rC(5)**2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**3 - &
(2*gammaM2*pi**2*Cos(pi*x*pC(5))*Cos(pi*x*rC(5))*pC(2)*pC(5)*rC(2)* &
rC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2 + &
(gammaM2*pi**2*rC(2)*rC(5)**2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))*Sin(pi*x*rC(5)))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2 - &
(gammaM2*pi**2*pC(2)*pC(5)**2*Sin(pi*x*pC(5)))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
((2*gammaM2*pi**2*Cos(pi*y*rC(6))**2*rC(3)**2*rC(6)**2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**3 - &
(2*gammaM2*pi**2*Cos(pi*y*pC(6))*Cos(pi*y*rC(6))*pC(3)*pC(6)*rC(3)* &
rC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2 + &
(gammaM2*pi**2*rC(3)*rC(6)**2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))*Sin(pi*y*rC(6)))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2 - &
(gammaM2*pi**2*pC(3)*pC(6)**2*Sin(pi*y*pC(6)))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
((2*gammaM2*pi**2*Cos(pi*z*rC(7))**2*rC(4)**2*rC(7)**2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**3 - &
(2*gammaM2*pi**2*Cos(pi*z*pC(7))*Cos(pi*z*rC(7))*pC(4)*pC(7)*rC(4)* &
rC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2 + &
(gammaM2*pi**2*rC(4)*rC(7)**2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))*Sin(pi*z*rC(7)))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2 - &
(gammaM2*pi**2*pC(4)*pC(7)**2*Sin(pi*z*pC(7)))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))))/((-1 + gamma)*Mach**2*Pr*Re))
Q(5) = Q(5) + & ! The statement is separated here for ifort not to crash
pi*Cos(pi*x*pC(5))*pC(2)*pC(5)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4)) &
+ pi*Cos(pi*x*uC(5))*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))*uC(2)*uC(5) + &
pi*Cos(pi*y*pC(6))*pC(3)*pC(6)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4)) &
+ pi*Cos(pi*y*vC(6))*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))*vC(3)*vC(6) + &
pi*Cos(pi*z*pC(7))*pC(4)*pC(7)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4))* &
((pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
((uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))**2 + &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))**2 + &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))**2)/2.) + &
pi*Cos(pi*x*uC(5))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*uC(2)*uC(5)* &
((pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
((uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))**2 + &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))**2 + &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))**2)/2.) + &
pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4))* &
((pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
((uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))**2 + &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))**2 + &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))**2)/2.) + &
pi*Cos(pi*y*vC(6))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*vC(3)*vC(6)* &
((pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
((uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))**2 + &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))**2 + &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))**2)/2.) + &
pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4))* &
((pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
((uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))**2 + &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))**2 + &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))**2)/2.) + &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + rC(4)*Sin(pi*z*rC(7)))* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4))* &
(-((pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2)) + &
(pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
(2*pi*Cos(pi*x*uC(5))*uC(2)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))*uC(5) + &
2*pi*Cos(pi*x*vC(5))*vC(2)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))*vC(5) + &
2*pi*Cos(pi*x*wC(5))*wC(2)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))*wC(5))/2.) + &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + rC(4)*Sin(pi*z*rC(7)))* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4))* &
(-((pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2)) + &
(pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
(2*pi*Cos(pi*y*uC(6))*uC(3)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))*uC(6) + &
2*pi*Cos(pi*y*vC(6))*vC(3)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))*vC(6) + &
2*pi*Cos(pi*y*wC(6))*wC(3)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))*wC(6))/2.) + &
pi*Cos(pi*z*wC(7))*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))*wC(4)*wC(7) + &
pi*Cos(pi*z*wC(7))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*wC(4)* &
((pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
((uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))**2 + &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))**2 + &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))**2)/2.)*wC(7) + &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + rC(4)*Sin(pi*z*rC(7)))* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4))* &
(-((pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2)) + &
(pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
(2*pi*Cos(pi*z*uC(7))*uC(4)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))*uC(7) + &
2*pi*Cos(pi*z*vC(7))*vC(4)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))*vC(7) + &
2*pi*Cos(pi*z*wC(7))*wC(4)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))*wC(7))/2.)
Q(5) = Q(5) - & ! The statement is separated here for ifort not to crash
(-((gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*y*uC(6))*uC(3)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))*uC(6)**2)/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))) - &
(gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*z*uC(7))*uC(4)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))*uC(7)**2)/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*x*vC(5))*vC(2)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))*vC(5)**2)/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*pC(6))*pC(3)*pC(6)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
(2.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*uC(6))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*uC(3)*uC(6)* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*pC(5))*pC(2)*pC(5)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
(2.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*vC(5))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*vC(2)*vC(5)* &
(pi*Cos(pi*y*uC(6))*uC(3)*uC(6) + pi*Cos(pi*x*vC(5))*vC(2)*vC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*z*vC(7))*vC(4)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))*vC(7)**2)/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*x*wC(5))*wC(2)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))*wC(5)**2)/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*pC(7))*pC(4)*pC(7)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
(2.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*uC(7))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*uC(4)*uC(7)* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*pC(5))*pC(2)*pC(5)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
(2.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*wC(5))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*wC(2)*wC(5)* &
(pi*Cos(pi*z*uC(7))*uC(4)*uC(7) + pi*Cos(pi*x*wC(5))*wC(2)*wC(5)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*y*wC(6))*wC(3)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))*wC(6)**2)/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*pC(7))*pC(4)*pC(7)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
(2.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*vC(7))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*vC(4)*vC(7)* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*pC(6))*pC(3)*pC(6)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*(1 + S_div_TRef_Sutherland)*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
(2.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*wC(6))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*wC(3)*wC(6)* &
(pi*Cos(pi*z*vC(7))*vC(4)*vC(7) + pi*Cos(pi*y*wC(6))*wC(3)*wC(6)))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
pi*Cos(pi*x*uC(5))*uC(2)*uC(5)* &
((2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*uC(5))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*uC(2)*uC(5))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(2*gammaM2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))) + &
pi*Cos(pi*y*vC(6))*vC(3)*vC(6)* &
((2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*vC(6))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*vC(3)*vC(6))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(2*gammaM2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)* &
((2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*wC(7))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*wC(4)*wC(7))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(2*gammaM2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))) + &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))* &
((-2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*uC(5))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*uC(2)*uC(5))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(2*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)*Cos(pi*x*rC(5))*Cos(pi*x*uC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*uC(2)*uC(5))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(2*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)*Cos(pi*x*pC(5))*Cos(pi*x*uC(5))*pC(2)*pC(5)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*uC(2)*uC(5))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*uC(5))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*uC(2)*uC(5))/ &
(Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(4*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*x*uC(5))*uC(2)*uC(5)**2)/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(2*gammaM2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) + &
(2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*x*pC(5))*pC(2)*pC(5)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))) + &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))* &
((-2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*vC(6))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*vC(3)*vC(6))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(2*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)*Cos(pi*y*rC(6))*Cos(pi*y*vC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*vC(3)*vC(6))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(2*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)*Cos(pi*y*pC(6))*Cos(pi*y*vC(6))*pC(3)*pC(6)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*vC(3)*vC(6))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*vC(6))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*vC(3)*vC(6))/ &
(Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(4*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*y*vC(6))*vC(3)*vC(6)**2)/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(2*gammaM2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) + &
(2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*y*pC(6))*pC(3)*pC(6)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))) + &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))* &
((-2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*wC(7))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*wC(4)*wC(7))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) - &
(2*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)*Cos(pi*z*rC(7))*Cos(pi*z*wC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*wC(4)*wC(7))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(2*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)*Cos(pi*z*pC(7))*Cos(pi*z*wC(7))*pC(4)*pC(7)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*wC(4)*wC(7))/ &
((rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*wC(7))* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*wC(4)*wC(7))/ &
(Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(4*gammaM2*pi**2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))*Sin(pi*z*wC(7))*wC(4)*wC(7)**2)/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) + &
(2*gammaM2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))**2) + &
(2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(2*gammaM2*pi*(1 + S_div_TRef_Sutherland)*Cos(pi*z*pC(7))*pC(4)*pC(7)* &
Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))) - &
(gammaM2*(1 + S_div_TRef_Sutherland)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))* &
(-((gammaM2*pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2) + &
(gammaM2*pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(pi*Cos(pi*x*uC(5))*uC(2)*uC(5) + pi*Cos(pi*y*vC(6))*vC(3)*vC(6) + &
pi*Cos(pi*z*wC(7))*wC(4)*wC(7)))/ &
(3.*Sqrt((gammaM2*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7))))* &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))* &
(S_div_TRef_Sutherland + (gammaM2* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))))))/Re
end associate
END SUBROUTINE ManufacturedSolutionSourceNS
!
!///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
!
SUBROUTINE ManufacturedSolutionSourceEuler( xx, t, Q )
!
! ------------------------
! Source term for MS Euler
! ------------------------
!
IMPLICIT NONE
REAL(KIND=RP) :: xx(3), t
REAL(KIND=RP) :: Q(NCONS)
REAL(KIND=RP) :: x, y, z
associate ( gamma => thermodynamics % gamma )
x = xx(1)
y = xx(2)
z = xx(3)
!
! -------------------------
! Mass equation Source term
! -------------------------
!
Q(1) = Q(1) + pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4)) &
+ pi*Cos(pi*x*uC(5))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*uC(2)*uC(5) + &
pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4)) &
+ pi*Cos(pi*y*vC(6))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*vC(3)*vC(6) + &
pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*z*wC(7))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*wC(4)*wC(7)
!
! -------------------------
! u-velocity Source term
! -------------------------
!
Q(2) = Q(2) + pi*Cos(pi*x*pC(5))*pC(2)*pC(5) + &
pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))**2 + &
2*pi*Cos(pi*x*uC(5))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*uC(2)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))*uC(5) + &
pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))*(vC(1) + Sin(pi*x*vC(5))*vC(2) + &
Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4)) + &
pi*Cos(pi*y*uC(6))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*uC(3)*uC(6)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4)) &
+ pi*Cos(pi*y*vC(6))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*(uC(1) + Sin(pi*x*uC(5))*uC(2) + &
Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4))*vC(3)*vC(6) + &
pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))*(wC(1) + Sin(pi*x*wC(5))*wC(2) + &
Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) + &
pi*Cos(pi*z*uC(7))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*uC(4)*uC(7)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*z*wC(7))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*(uC(1) + Sin(pi*x*uC(5))*uC(2) + &
Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4))*wC(4)*wC(7)
!
! -------------------------
! v-velocity Source term
! -------------------------
!
Q(3) = Q(3) + pi*Cos(pi*y*pC(6))*pC(3)*pC(6) + &
pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))*(vC(1) + Sin(pi*x*vC(5))*vC(2) + &
Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4)) + &
pi*Cos(pi*x*uC(5))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*uC(2)*uC(5)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4)) &
+ pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))**2 + &
pi*Cos(pi*x*vC(5))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*(uC(1) + Sin(pi*x*uC(5))*uC(2) + &
Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4))*vC(2)*vC(5) + &
2*pi*Cos(pi*y*vC(6))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*vC(3)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))*vC(6) + &
pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))*(wC(1) + Sin(pi*x*wC(5))*wC(2) + &
Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) + &
pi*Cos(pi*z*vC(7))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*vC(4)*vC(7)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*z*wC(7))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*(vC(1) + Sin(pi*x*vC(5))*vC(2) + &
Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4))*wC(4)*wC(7)
!
! -------------------------
! w-velocity Source term
! -------------------------
!
Q(4) = Q(4) + pi*Cos(pi*z*pC(7))*pC(4)*pC(7) + &
pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))*(wC(1) + Sin(pi*x*wC(5))*wC(2) + &
Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) + &
pi*Cos(pi*x*uC(5))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*uC(2)*uC(5)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))*(wC(1) + Sin(pi*x*wC(5))*wC(2) + &
Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) + &
pi*Cos(pi*y*vC(6))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*vC(3)*vC(6)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))**2 + &
pi*Cos(pi*x*wC(5))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*(uC(1) + Sin(pi*x*uC(5))*uC(2) + &
Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4))*wC(2)*wC(5) + &
pi*Cos(pi*y*wC(6))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*(vC(1) + Sin(pi*x*vC(5))*vC(2) + &
Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4))*wC(3)*wC(6) + &
2*pi*Cos(pi*z*wC(7))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*wC(4)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))*wC(7)
!
! -------------------------
! Energy Source term
! -------------------------
!
Q(5) = Q(5) + pi*Cos(pi*x*pC(5))*pC(2)*pC(5)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + Sin(pi*z*uC(7))*uC(4)) &
+ pi*Cos(pi*x*uC(5))*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))*uC(2)*uC(5) + &
pi*Cos(pi*y*pC(6))*pC(3)*pC(6)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + Sin(pi*z*vC(7))*vC(4)) &
+ pi*Cos(pi*y*vC(6))*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))*vC(3)*vC(6) + &
pi*Cos(pi*z*pC(7))*pC(4)*pC(7)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + Sin(pi*z*wC(7))*wC(4)) &
+ pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))*((pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
((uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))**2 + &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))**2 + &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))**2)/2.) + &
pi*Cos(pi*x*uC(5))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*uC(2)*uC(5)* &
((pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
((uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))**2 + &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))**2 + &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))**2)/2.) + &
pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))*((pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
((uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))**2 + &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))**2 + &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))**2)/2.) + &
pi*Cos(pi*y*vC(6))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*vC(3)*vC(6)* &
((pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
((uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))**2 + &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))**2 + &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))**2)/2.) + &
pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))*((pC(1) + pC(2)*Sin(pi*x*pC(5)) + &
pC(3)*Sin(pi*y*pC(6)) + pC(4)*Sin(pi*z*pC(7)))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
((uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))**2 + &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))**2 + &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))**2)/2.) + &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + rC(4)*Sin(pi*z*rC(7)))* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))*(-((pi*Cos(pi*x*rC(5))*rC(2)*rC(5)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2)) + &
(pi*Cos(pi*x*pC(5))*pC(2)*pC(5))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
(2*pi*Cos(pi*x*uC(5))*uC(2)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))*uC(5) + &
2*pi*Cos(pi*x*vC(5))*vC(2)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))*vC(5) + &
2*pi*Cos(pi*x*wC(5))*wC(2)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))*wC(5))/2.) + &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + rC(4)*Sin(pi*z*rC(7)))* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))*(-((pi*Cos(pi*y*rC(6))*rC(3)*rC(6)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2)) + &
(pi*Cos(pi*y*pC(6))*pC(3)*pC(6))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
(2*pi*Cos(pi*y*uC(6))*uC(3)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))*uC(6) + &
2*pi*Cos(pi*y*vC(6))*vC(3)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))*vC(6) + &
2*pi*Cos(pi*y*wC(6))*wC(3)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))*wC(6))/2.) + &
pi*Cos(pi*z*wC(7))*(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))*wC(4)*wC(7) + &
pi*Cos(pi*z*wC(7))*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))*wC(4)* &
((pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7)))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
((uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))**2 + &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))**2 + &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))**2)/2.)*wC(7) + &
(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + rC(4)*Sin(pi*z*rC(7)))* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))*(-((pi*Cos(pi*z*rC(7))*rC(4)*rC(7)* &
(pC(1) + pC(2)*Sin(pi*x*pC(5)) + pC(3)*Sin(pi*y*pC(6)) + &
pC(4)*Sin(pi*z*pC(7))))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))**2)) + &
(pi*Cos(pi*z*pC(7))*pC(4)*pC(7))/ &
((-1 + gamma)*(rC(1) + rC(2)*Sin(pi*x*rC(5)) + rC(3)*Sin(pi*y*rC(6)) + &
rC(4)*Sin(pi*z*rC(7)))) + &
(2*pi*Cos(pi*z*uC(7))*uC(4)* &
(uC(1) + Sin(pi*x*uC(5))*uC(2) + Sin(pi*y*uC(6))*uC(3) + &
Sin(pi*z*uC(7))*uC(4))*uC(7) + &
2*pi*Cos(pi*z*vC(7))*vC(4)* &
(vC(1) + Sin(pi*x*vC(5))*vC(2) + Sin(pi*y*vC(6))*vC(3) + &
Sin(pi*z*vC(7))*vC(4))*vC(7) + &
2*pi*Cos(pi*z*wC(7))*wC(4)* &
(wC(1) + Sin(pi*x*wC(5))*wC(2) + Sin(pi*y*wC(6))*wC(3) + &
Sin(pi*z*wC(7))*wC(4))*wC(7))/2.)
end associate
END SUBROUTINE ManufacturedSolutionSourceEuler
END MODULE ManufacturedSolutionsNS
