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/*@@
@file GRHydro_Tmunu.F90
@date Aug 30, 2010
@author Joshua Faber, Scott Noble, Bruno Mundim, 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 +b^2) u u + (P+b^2/2) g - b b
mu nu 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)
#define Bvecx(i,j,k) Bvec(i,j,k,1)
#define Bvecy(i,j,k) Bvec(i,j,k,2)
#define Bvecz(i,j,k) Bvec(i,j,k,3)
#define bcomx(i,j,k) bcom(i,j,k,1)
#define bcomy(i,j,k) bcom(i,j,k,2)
#define bcomz(i,j,k) bcom(i,j,k,3)
subroutine GRHydro_TmunuM(CCTK_ARGUMENTS)
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
CCTK_REAL :: velxlow, velylow, velzlow
CCTK_REAL :: betaxlow, betaylow, betazlow, beta2
CCTK_REAL :: Bvecxlow,Bvecylow,Bveczlow
CCTK_REAL :: bdotv,b2,bxlow,bylow,bzlow,btlow,dum1,dum2
CCTK_REAL :: utlow,rhohstarw2,pstar
CCTK_REAL :: bdotbeta,vdotbeta
CCTK_INT :: i,j,k
!$OMP PARALLEL DO PRIVATE(i,j,k,velxlow, velylow, velzlow,&
!$OMP Bvecxlow,Bvecylow,Bveczlow, bdotv,dum1,dum2,b2,bxlow,bylow,bzlow,&
!$OMP betaxlow, betaylow, betazlow, beta2, bdotbeta,vdotbeta,utlow, btlow,&
!$OMP rhohstarw2,pstar)
do k = 1, cctk_lsh(3)
do j = 1, cctk_lsh(2)
do i = 1, cctk_lsh(1)
! need separate dum1, dum2 b/c of Fortrans aliasing rules
call calc_vlow_blow(gxx(i,j,k),gxy(i,j,k),gxz(i,j,k),&
gyy(i,j,k),gyz(i,j,k),gzz(i,j,k), &
velx(i,j,k),vely(i,j,k),velz(i,j,k),Bvecx(i,j,k),Bvecy(i,j,k),Bvecz(i,j,k), &
velxlow,velylow,velzlow,Bvecxlow,Bvecylow,Bveczlow, &
bdotv,b2,dum1,dum2,bxlow,bylow,bzlow)
!!$ Calculate lower components and square of shift vector.
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
bdotbeta = betaxlow*Bvecx(i,j,k)+betaylow*Bvecy(i,j,k)+betazlow*Bvecz(i,j,k)
vdotbeta = betaxlow*velx(i,j,k)+betaylow*vely(i,j,k)+betazlow*velz(i,j,k)
!!$ u0 low is missing the w_lorentz factor (see below)!!
utlow = -1.d0*alp(i,j,k) + vdotbeta
btlow = -1.0d0*w_lorentz(i,j,k)*alp(i,j,k)*bdotv + &
bdotbeta/w_lorentz(i,j,k) + w_lorentz(i,j,k)*bdotv*vdotbeta
!!$ Calculate the specific relativistic enthalpy times rho + the mag. field contribution times the
!!$ square of the lorentz factor.
rhohstarw2 = w_lorentz(i,j,k)**2*(rho(i,j,k)*(1.0d0 + eps(i,j,k)) + press(i,j,k) + b2)
pstar = press(i,j,k)+0.5d0*b2
!!$ Calculate lower components of 4-velocity (without the Lorent factor).
!!$ uxlow = velxlow
!!$ uylow = velylow
!!$ uzlow = velzlow
!!$ Calculate Tmunu (the lower components!).
eTtt(i,j,k) = eTtt(i,j,k) + rhohstarw2*utlow**2 + pstar*(beta2 - alp(i,j,k)**2) - btlow**2
eTtx(i,j,k) = eTtx(i,j,k) + rhohstarw2*utlow*velxlow + pstar*betaxlow - btlow*bxlow
eTty(i,j,k) = eTty(i,j,k) + rhohstarw2*utlow*velylow + pstar*betaylow - btlow*bylow
eTtz(i,j,k) = eTtz(i,j,k) + rhohstarw2*utlow*velzlow + pstar*betazlow - btlow*bzlow
eTxx(i,j,k) = eTxx(i,j,k) + rhohstarw2*velxlow**2 + pstar*gxx(i,j,k) - bxlow**2
eTyy(i,j,k) = eTyy(i,j,k) + rhohstarw2*velylow**2 + pstar*gyy(i,j,k) - bylow**2
eTzz(i,j,k) = eTzz(i,j,k) + rhohstarw2*velzlow**2 + pstar*gzz(i,j,k) - bzlow**2
eTxy(i,j,k) = eTxy(i,j,k) + rhohstarw2*velxlow*velylow + pstar*gxy(i,j,k) - bxlow*bylow
eTxz(i,j,k) = eTxz(i,j,k) + rhohstarw2*velxlow*velzlow + pstar*gxz(i,j,k) - bxlow*bzlow
eTyz(i,j,k) = eTyz(i,j,k) + rhohstarw2*velylow*velzlow + pstar*gyz(i,j,k) - bylow*bzlow
if(calculate_bcom .ne. 0) then
bcom_sq(i,j,k) = b2
bcom0(i,j,k) = w_lorentz(i,j,k)*bdotv/alp(i,j,k)
bcomx(i,j,k) = Bvecx(i,j,k)/w_lorentz(i,j,k) + bcom0(i,j,k)*(alp(i,j,k)*velx(i,j,k)-betax(i,j,k))
bcomy(i,j,k) = Bvecy(i,j,k)/w_lorentz(i,j,k) + bcom0(i,j,k)*(alp(i,j,k)*vely(i,j,k)-betay(i,j,k))
bcomz(i,j,k) = Bvecz(i,j,k)/w_lorentz(i,j,k) + bcom0(i,j,k)*(alp(i,j,k)*velz(i,j,k)-betaz(i,j,k))
endif
end do
end do
end do
!$OMP END PARALLEL DO
return
end subroutine GRHydro_TmunuM
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