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/*@@
@file GRHydro_Tmunu.F90
@date Thu Apr 16 19:38:40 2009
@author Ian Hawke
@histpry
Apr. 2009: Luca Baiotti copied and adapted for the Tmunu-thorn mechanism the original include file
@desc
The calculation of the stress energy tensor.
The version used here was worked out by Miguel Alcubierre. I
think it was an extension of the routine from GR3D, written
by Mark Miller.
C version added by Ian Hawke.
Lower components of the stress-energy tensor obtained from
the hydro variables. The components are given by:
T = rho h u u + P g
mu nu mu nu mu nu
where rho is the energy density of the fluid, h the enthalpy
and P the pressure. The enthalpy is given in terms of the
basic variables as:
h = 1 + e + P/rho
with e the internal energy (eps here).
In the expresion for T_{mu,nu} we also have the four-velocity
of the fluid given by (v_i is the 3-velocity field):
i
u = W ( - alpha + v beta )
0 i
u = W v
i i
i -1/2
with W the Lorentz factor: W = ( 1 - v v )
i
and where alpha and beta are the lapse and shift vector.
Finally, the 4 metric is given by
2 i
g = - alpha + beta beta
00 i
g = beta
0i i
g = gamma (the spatial metric)
ij ij
@enddesc
@@*/
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Parameters.h"
#include "SpaceMask.h"
#define velx(i,j,k) vel(i,j,k,1)
#define vely(i,j,k) vel(i,j,k,2)
#define velz(i,j,k) vel(i,j,k,3)
subroutine GRHydro_Tmunu(CCTK_ARGUMENTS)
implicit none
DECLARE_CCTK_ARGUMENTS
CCTK_REAL velxlow, velylow, velzlow
CCTK_REAL betaxlow, betaylow, betazlow, beta2
CCTK_REAL utlow, uxlow, uylow, uzlow
CCTK_REAL rhoenthalpy
CCTK_REAL ut,ux,uy,uz,bst,bsx,bsy,bsz,bs2
CCTK_INT i,j,k
!$OMP PARALLEL DO PRIVATE(i,j,velxlow, velylow, velzlow,&
!$OMP betaxlow, betaylow, betazlow, beta2, utlow, uxlow, uylow, uzlow,&
!$OMP rhoenthalpy, ut,ux,uy,uz,bst,bsx,bsy,bsz,bs2)
do k = 1, cctk_lsh(3)
do j = 1, cctk_lsh(2)
do i = 1, cctk_lsh(1)
velxlow = gxx(i,j,k)*velx(i,j,k) + gxy(i,j,k)*vely(i,j,k) + gxz(i,j,k)*velz(i,j,k)
velylow = gxy(i,j,k)*velx(i,j,k) + gyy(i,j,k)*vely(i,j,k) + gyz(i,j,k)*velz(i,j,k)
velzlow = gxz(i,j,k)*velx(i,j,k) + gyz(i,j,k)*vely(i,j,k) + gzz(i,j,k)*velz(i,j,k)
!!$ Calculate lower components and square of shift vector.
if (shift_state .ne. 0) then
betaxlow = gxx(i,j,k)*betax(i,j,k) + gxy(i,j,k)*betay(i,j,k) + gxz(i,j,k)*betaz(i,j,k)
betaylow = gxy(i,j,k)*betax(i,j,k) + gyy(i,j,k)*betay(i,j,k) + gyz(i,j,k)*betaz(i,j,k)
betazlow = gxz(i,j,k)*betax(i,j,k) + gyz(i,j,k)*betay(i,j,k) + gzz(i,j,k)*betaz(i,j,k)
beta2 = betax(i,j,k)*betaxlow + betay(i,j,k)*betaylow + betaz(i,j,k)*betazlow
else
betaxlow = 0.0D0
betaylow = 0.0D0
betazlow = 0.0D0
beta2 = 0.0D0
end if
!!$ Calculate the specific relativistic enthalpy times rho times the
!!$ square of the lorentz factor.
rhoenthalpy = w_lorentz(i,j,k)**2*(rho(i,j,k)*(1.0D0 + eps(i,j,k)) + press(i,j,k))
!!$ Calculate lower components of 4-velocity (without the Lorent factor).
utlow = (-alp(i,j,k) + velx(i,j,k)*betaxlow + vely(i,j,k)*betaylow + velz(i,j,k)*betazlow)
uxlow = velxlow
uylow = velylow
uzlow = velzlow
!!$ Calculate Tmunu (the lower components!).
eTtt(i,j,k) = eTtt(i,j,k) + rhoenthalpy*utlow**2 + press(i,j,k)*(beta2 - alp(i,j,k)**2)
eTtx(i,j,k) = eTtx(i,j,k) + rhoenthalpy*utlow*uxlow + press(i,j,k)*betaxlow
eTty(i,j,k) = eTty(i,j,k) + rhoenthalpy*utlow*uylow + press(i,j,k)*betaylow
eTtz(i,j,k) = eTtz(i,j,k) + rhoenthalpy*utlow*uzlow + press(i,j,k)*betazlow
eTxx(i,j,k) = eTxx(i,j,k) + rhoenthalpy*uxlow**2 + press(i,j,k)*gxx(i,j,k)
eTyy(i,j,k) = eTyy(i,j,k) + rhoenthalpy*uylow**2 + press(i,j,k)*gyy(i,j,k)
eTzz(i,j,k) = eTzz(i,j,k) + rhoenthalpy*uzlow**2 + press(i,j,k)*gzz(i,j,k)
eTxy(i,j,k) = eTxy(i,j,k) + rhoenthalpy*uxlow*uylow + press(i,j,k)*gxy(i,j,k)
eTxz(i,j,k) = eTxz(i,j,k) + rhoenthalpy*uxlow*uzlow + press(i,j,k)*gxz(i,j,k)
eTyz(i,j,k) = eTyz(i,j,k) + rhoenthalpy*uylow*uzlow + press(i,j,k)*gyz(i,j,k)
end do
end do
end do
!$OMP END PARALLEL DO
return
end subroutine GRHydro_Tmunu
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