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/*@@
@file GRHydro_EMTensor.inc
@date Sat Jan 26 02:03:56 2002
@author Ian Hawke
@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
@@*/
#ifdef FCODE
/* if (SpaceMask_CheckStateBitsF90(space_mask, i,j,k, \
atmosphere_field_descriptor, \
atmosphere_normal_descriptor)) then*/
!!$ call SpaceMask_GetTypeBits(type_bits, "Hydro_Atmosphere")
!!$ call SpaceMask_GetStateBits(atmosphere, "Hydro_Atmosphere", "in_atmosphere")
if (conformal_state .eq. 0) then
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)
else
velxlow = psi(i,j,k)**4 * (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 = psi(i,j,k)**4 * (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 = psi(i,j,k)**4 * (gxz(i,j,k)*velx(i,j,k) + gyz(i,j,k)*vely(i,j,k) + gzz(i,j,k)*velz(i,j,k) )
end if
!!$ Calculate lower components and square of shift vector.
if (shift_state .ne. 0) then
if (conformal_state .eq. 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)
else
betaxlow = psi(i,j,k)**4 * (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 = psi(i,j,k)**4 * (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 = psi(i,j,k)**4 * (gxz(i,j,k)*betax(i,j,k) + gyz(i,j,k)*betay(i,j,k) + gzz(i,j,k)*betaz(i,j,k) )
end if
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!).
!!$ if ( .not.(SpaceMask_CheckStateBitsF90(space_mask, i, j, k, type_bits, atmosphere) )) then
Ttt = Ttt + rhoenthalpy*utlow**2 + press(i,j,k)*(beta2 - alp(i,j,k)**2)
Ttx = Ttx + rhoenthalpy*utlow*uxlow + press(i,j,k)*betaxlow
Tty = Tty + rhoenthalpy*utlow*uylow + press(i,j,k)*betaylow
Ttz = Ttz + rhoenthalpy*utlow*uzlow + press(i,j,k)*betazlow
if (conformal_state .eq. 0) then
Txx = Txx + rhoenthalpy*uxlow**2 + press(i,j,k)*gxx(i,j,k)
Tyy = Tyy + rhoenthalpy*uylow**2 + press(i,j,k)*gyy(i,j,k)
Tzz = Tzz + rhoenthalpy*uzlow**2 + press(i,j,k)*gzz(i,j,k)
Txy = Txy + rhoenthalpy*uxlow*uylow + press(i,j,k)*gxy(i,j,k)
Txz = Txz + rhoenthalpy*uxlow*uzlow + press(i,j,k)*gxz(i,j,k)
Tyz = Tyz + rhoenthalpy*uylow*uzlow + press(i,j,k)*gyz(i,j,k)
else
Txx = Txx + rhoenthalpy*uxlow**2 + psi(i,j,k)**4 * press(i,j,k)*gxx(i,j,k)
Tyy = Tyy + rhoenthalpy*uylow**2 + psi(i,j,k)**4 * press(i,j,k)*gyy(i,j,k)
Tzz = Tzz + rhoenthalpy*uzlow**2 + psi(i,j,k)**4 * press(i,j,k)*gzz(i,j,k)
Txy = Txy + rhoenthalpy*uxlow*uylow + psi(i,j,k)**4 * press(i,j,k)*gxy(i,j,k)
Txz = Txz + rhoenthalpy*uxlow*uzlow + psi(i,j,k)**4 * press(i,j,k)*gxz(i,j,k)
Tyz = Tyz + rhoenthalpy*uylow*uzlow + psi(i,j,k)**4 * press(i,j,k)*gyz(i,j,k)
end if
!!$ end if
/* end if*/
#endif
#ifdef CCODE
if (!*conformal_state)
{
velxlow = gxx[ijk]*velx[ijk] + gxy[ijk]*vely[ijk] +
gxz[ijk]*velz[ijk];
velylow = gxy[ijk]*velx[ijk] + gyy[ijk]*vely[ijk] +
gyz[ijk]*velz[ijk];
velzlow = gxz[ijk]*velx[ijk] + gyz[ijk]*vely[ijk] +
gzz[ijk]*velz[ijk];
}
else
{
velxlow = pow(psi[ijk],4) * (gxx[ijk]*velx[ijk] +
gxy[ijk]*vely[ijk] +
gxz[ijk]*velz[ijk]);
velylow = pow(psi[ijk],4) * (gxy[ijk]*velx[ijk] +
gyy[ijk]*vely[ijk] +
gyz[ijk]*velz[ijk]);
velzlow = pow(psi[ijk],4) * (gxz[ijk]*velx[ijk] +
gyz[ijk]*vely[ijk] +
gzz[ijk]*velz[ijk]);
}
/*
* Calculate lower components and square of shift vector.
*/
if (*shift_state)
{
if (!*conformal_state)
{
betaxlow = gxx[ijk]*betax[ijk] + gxy[ijk]*betay[ijk]
+ gxz[ijk]*betaz[ijk];
betaylow = gxy[ijk]*betax[ijk] + gyy[ijk]*betay[ijk]
+ gyz[ijk]*betaz[ijk];
betazlow = gxz[ijk]*betax[ijk] + gyz[ijk]*betay[ijk]
+ gzz[ijk]*betaz[ijk];
}
else
{
betaxlow = pow(psi[ijk],4) * (gxx[ijk]*betax[ijk] +
gxy[ijk]*betay[ijk] +
gxz[ijk]*betaz[ijk]);
betaylow = pow(psi[ijk],4) * (gxy[ijk]*betax[ijk] +
gyy[ijk]*betay[ijk] +
gyz[ijk]*betaz[ijk]);
betazlow = pow(psi[ijk],4) * (gxz[ijk]*betax[ijk] +
gyz[ijk]*betay[ijk] +
gzz[ijk]*betaz[ijk]);
}
beta2 = betax[ijk]*betaxlow + betay[ijk]*betaylow
+ betaz[ijk]*betazlow ;
}
else
{
betaxlow = 0.0;
betaylow = 0.0;
betazlow = 0.0;
beta2 = 0.0;
}
/*
* Calculate the specific relativistic enthalpy times rho times the
* square of the lorentz factor.
*/
rhoenthalpy = w_lorentz[ijk]*w_lorentz[ijk]*
(rho[ijk]*(1.0 + eps[ijk]) + press[ijk]);
/*
* Calculate lower components of 4-velocity (without the Lorent factor).
*/
utlow = (-alp[ijk] + velx[ijk]*betaxlow + vely[ijk]*betaylow
+ velz[ijk]*betazlow);
uxlow = velxlow;
uylow = velylow;
uzlow = velzlow;
/*
* Calculate Tmunu (the lower components!).
*/
Ttt = Ttt + rhoenthalpy*utlow*utlow +
press[ijk]*(beta2 - alp[ijk]*alp[ijk]);
Ttx = Ttx + rhoenthalpy*utlow*uxlow + press[ijk]*betaxlow;
Tty = Tty + rhoenthalpy*utlow*uylow + press[ijk]*betaylow;
Ttz = Ttz + rhoenthalpy*utlow*uzlow + press[ijk]*betazlow;
if (!*conformal_state)
{
Txx = Txx + rhoenthalpy*uxlow*uxlow + press[ijk]*gxx[ijk];
Tyy = Tyy + rhoenthalpy*uylow*uylow + press[ijk]*gyy[ijk];
Tzz = Tzz + rhoenthalpy*uzlow*uzlow + press[ijk]*gzz[ijk];
Txy = Txy + rhoenthalpy*uxlow*uylow + press[ijk]*gxy[ijk];
Txz = Txz + rhoenthalpy*uxlow*uzlow + press[ijk]*gxz[ijk];
Tyz = Tyz + rhoenthalpy*uylow*uzlow + press[ijk]*gyz[ijk];
}
else
{
Txx = Txx + rhoenthalpy*uxlow*uxlow +
pow(psi[ijk],4) * press[ijk]*gxx[ijk];
Tyy = Tyy + rhoenthalpy*uylow*uylow +
pow(psi[ijk],4) * press[ijk]*gyy[ijk];
Tzz = Tzz + rhoenthalpy*uzlow*uzlow +
pow(psi[ijk],4) * press[ijk]*gzz[ijk];
Txy = Txy + rhoenthalpy*uxlow*uylow +
pow(psi[ijk],4) * press[ijk]*gxy[ijk];
Txz = Txz + rhoenthalpy*uxlow*uzlow +
pow(psi[ijk],4) * press[ijk]*gxz[ijk];
Tyz = Tyz + rhoenthalpy*uylow*uzlow +
pow(psi[ijk],4) * press[ijk]*gyz[ijk];
}
#endif
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