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|
C Here we added the matter variables for several of the metrics
C you can find in "src" directory through the components of the
C stress-eergy tensor. Being different in specific cases it is
C necessary to check first which metric is running.
C Author : Dumitru Vulcanov (Timisoara, Romania)
C $Header$
C Varianta cu un singur param. (raza initiala) pt Rob-Walker
#include "param_defs.inc"
c
c FIXME:
c If we could be certain that this code were always compiled as Fortran 90,
c the decode here could be done with a case statement, which ought to give
c better performance than the if-else chain we use now. But in practice
c Cactus has enough other overheads that this is not bothering with...
c
c
c ***** KLUDGE *****
c
c This code is #include-d into various evolution thorns, and alas does not
c have direct access to thorn Exact parameters. Instead, this code must
c use the restricted-grid-scalar copies of the parameters. In practice,
c this means changing "__" to "___" in all parameter names (but not in the
c #define constants in "param_defs.inc"). See the comments in param.ccl
c for further information on this.
c
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
ccccc Minkowski spacetime cccccccccccccccccccccccccccccccccccccccccccccccccccccc
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
if (decoded_exact_model .eq. EXACT__Minkowski) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Minkowski_shift) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Minkowski_funny) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Minkowski_gauge_wave) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Minkowski_conf_wave) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
ccccc black hole spacetimes cccccccccccccccccccccccccccccccccccccccccccccccccccc
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
elseif (decoded_exact_model .eq. EXACT__Schwarzschild_EF) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Schwarzschild_PG) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Schwarzschild_Novikov) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Kerr_BoyerLindquist) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Kerr_KerrSchild) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c Schwarzschild-Lemaitre spacetime
c (Schwarzschild black hole with cosmological constant)
c
elseif (decoded_exact_model .eq. EXACT__Schwarzschild_Lemaitre) then
razsch2=x(i,j,k)*x(i,j,k)+y(i,j,k)*y(i,j,k)+z(i,j,k)*z(i,j,k)
coefsch=-Schwarzschild_Lemaitre___Lambda/(8.0D0*pi)
pppsch=1.0D0-2.0D0*Schwarzschild_Lemaitre___mass/sqrt(razsch2)
& -Schwarzschild_Lemaitre___Lambda*razsch2/3.0D0
unusch=(1.0D0-pppsch)/pppsch/razsch2
Ttt = Ttt-coefsch*pppsch
Ttx = Ttx
Tty = Tty
Ttz = Ttz
Txx = Txx+coefsch*(1.0D0+x(i,j,k)*x(i,j,k)*unusch)
Tyy = Tyy+coefsch*(1.0D0+y(i,j,k)*y(i,j,k)*unusch)
Tzz = Tzz+coefsch*(1.0D0+z(i,j,k)*z(i,j,k)*unusch)
Txy = Txy+coefsch*x(i,j,k)*y(i,j,k)*unusch
Txz = Txz+coefsch*x(i,j,k)*z(i,j,k)*unusch
Tyz = Tyz+coefsch*y(i,j,k)*z(i,j,k)*unusch
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
elseif (decoded_exact_model .eq. EXACT__multi_BH) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Alvi) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Thorne_fakebinary) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
ccccc cosmological spacetimes cccccccccccccccccccccccccccccccccccccccccccccccccc
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c Lemaitre spacetime
c
elseif (decoded_exact_model .eq. EXACT__Lemaitre) then
unu1 = sqrt(3.0D0*Lemaitre___Lambda)
& * CCTK_time * (Lemaitre___kappa+1.0D0) / (2.0D0)
raz = Lemaitre___R0*(cosh(unu1)
& + sqrt(1.0D0+8.0D0*pi*Lemaitre___epsilon0
& /Lemaitre___Lambda)
& *sinh(unu1))
& **(2.0D0/(3.0D0*Lemaitre___kappa+3.0D0))
raz2 = raz*raz
treiori = -Lemaitre___Lambda*raz2/8.0D0/pi
& +Lemaitre___epsilon0*Lemaitre___kappa
& *raz**(-3.0D0*Lemaitre___kappa-1.0D0)
Ttt = Ttt + Lemaitre___Lambda/8.0D0/pi
& + Lemaitre___epsilon0*raz**(-3.0D0*(Lemaitre___kappa+1.0D0))
Txx = Txx + treiori
Tyy = Tyy + treiori
Tzz = Tzz + treiori
Txy = Txy
Tyz = Tyz
Txz = Txz
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
ccc
ccc this metric doesn't work and has been moved to ../../archive/
ccc
ccc Robertson-Walker spacetime
ccc
cc elseif (decoded_exact_model .eq. EXACT__Robertson_Walker) then
cc rr2 = x(i,j,k)*x(i,j,k)+y(i,j,k)*y(i,j,k)+z(i,j,k)*z(i,j,k)
cc
cc if (Robertson_Walker___pressure .gt. 0) then
cc aha1 = Robertson_Walker___k * (Robertson_Walker___R0**2)
cc & / (8.0D0*pi*(raza(i,j,k)**2))
cc aha2 = Robertson_Walker___k/(1.0D0 - Robertson_Walker___k*rr2)
cc
cc Ttt = Ttt + 3.0D0*aha1/(raza(i,j,k)*raza(i,j,k))
cc Txx = Txx + aha1*(1.0D0 + aha2*x(i,j,k)*x(i,j,k))
cc Tyy = Tyy + aha1*(1.0D0 + aha2*y(i,j,k)*y(i,j,k))
cc Tzz = Tzz + aha1*(1.0D0 + aha2*z(i,j,k)*z(i,j,k))
cc Txy = Txy + aha1*aha2*x(i,j,k)*y(i,j,k)
cc Txz = Txz + aha1*aha2*x(i,j,k)*z(i,j,k)
cc Tyz = Tyz + aha1*aha2*y(i,j,k)*y(i,j,k)
cc else
cc Ttt = Ttt+Robertson_Walker___rho * (Robertson_Walker___R0**3)
cc & / (raza(i,j,k)**3)
cc Txx = Txx
cc Tyy = Tyy
cc Tzz = Tzz
cc Txy = Txy
cc Txz = Txz
cc Tyz = Tyz
cc endif
cc
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c de Sitter spacetime
c
elseif (decoded_exact_model .eq. EXACT__de_Sitter) then
Ttt = Ttt + 1.0D0/6.0D0/pi/(CCTK_time**2)
Ttx = Ttx
Tty = Tty
Ttz = Ttz
Txx = Txx
Tyy = Tyy
Tzz = Tzz
Txy = Txy
Txz = Txz
Tyz = Tyz
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c de Sitter spacetime with cosmological constant
c
elseif (decoded_exact_model .eq. EXACT__de_Sitter_Lambda) then
aaaa = de_Sitter_Lambda___scale/(8.0D0*pi)
bbbb = aaaa*exp(2.0D0*sqrt(de_Sitter_Lambda___scale/3.0D0)*CCTK_time)
Ttt = Ttt + aaaa
Ttx = Ttx
Tty = Tty
Ttz = Ttz
Txx = Txx - bbbb
Tyy = Tyy - bbbb
Tzz = Tzz - bbbb
Txy = Txy
Txz = Txz
Tyz = Tyz
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c anti-de Sitter spacetime with cosmological constant
c
elseif (decoded_exact_model .eq. EXACT__anti_de_Sitter_Lambda) then
aaaa1 = anti_de_Sitter_Lambda___scale/(8.0D0*pi)
bbbb1 = aaaa1*exp(2.0D0*sqrt(-anti_de_Sitter_Lambda___scale/3.0D0)
& *x(i,j,k))
Ttt = Ttt + bbbb1
Ttx = Ttx
Tty = Tty
Ttz = Ttz
Txx = Txx - aaaa1
Tyy = Tyy - bbbb1
Tzz = Tzz - bbbb1
Txy = Txy
Txz = Txz
Tyz = Tyz
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
elseif (decoded_exact_model .eq. EXACT__Bianchi_I) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__Goedel) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c Bertotti spacetime
c
elseif (decoded_exact_model .eq. EXACT__Bertotti) then
bass = Bertotti___Lambda/(8.0D0*pi)
term1 = bass*exp(2.0D0*sqrt(-Bertotti___Lambda)*x(i,j,k))
term2 = bass*exp(2.0D0*sqrt(-Bertotti___Lambda)*z(i,j,k))
Ttt = Ttt + term1
Ttx = Ttx
Tty = Tty
Ttz = Ttz
Txx = Txx - bass
Tyy = Tyy - term2
Tzz = Tzz - bass
Txy = Txy
Txz = Txz
Tyz = Tyz
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c Kasner-like spacetime
c
elseif (decoded_exact_model .eq. EXACT__Kasner_like) then
kkkk=Kasner_like___q*(2.0D0-3.0D0*Kasner_like___q)
& /(8.0D0*pi*(CCTK_time**2))
Ttt = Ttt + kkkk
Ttx = Ttx
Tty = Tty
Ttz = Ttz
Txx = Txx + kkkk*CCTK_time**(2.0D0*Kasner_like___q)
Tyy = Tyy + kkkk*CCTK_time**(2.0D0*Kasner_like___q)
Tzz = Tzz + kkkk*CCTK_time**(2.0D0-4.0D0*Kasner_like___q)
Txy = Txy
Txz = Txz
Tyz = Tyz
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
elseif (decoded_exact_model .eq. EXACT__Kasner_axisymmetric) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c generalized Kasner spacetime
c
elseif (decoded_exact_model .eq. EXACT__Kasner_generalized) then
kkkk1 = ( Kasner_generalized___p1 - Kasner_generalized___p1**2
& + Kasner_generalized___p2 - Kasner_generalized___p2**2
& - Kasner_generalized___p1*Kasner_generalized___p2 )
& / (8.0D0*pi*(CCTK_time**2))
Ttt = Ttt + kkkk1
Ttx = Ttx
Tty = Tty
Ttz = Ttz
Txx = Txx+kkkk1*CCTK_time**(2.0D0*Kasner_generalized___p1)
Tyy = Tyy+kkkk1*CCTK_time**(2.0D0*Kasner_generalized___p2)
Tzz = Tzz+kkkk1*CCTK_time**(2.0D0-2.0D0*Kasner_generalized___p1
& -2.0D0*Kasner_generalized___p2)
Txy = Txy
Txz = Txz
Tyz = Tyz
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
elseif (decoded_exact_model .eq. EXACT__Gowdy_wave) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
elseif (decoded_exact_model .eq. EXACT__Milne) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
ccccc miscellaneous spacetimes ccccccccccccccccccccccccccccccccccccccccccccccccc
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
elseif (decoded_exact_model .eq. EXACT__boost_rotation_symmetric) then
c no stress-energy tensor in this model
elseif (decoded_exact_model .eq. EXACT__bowl) then
c no stress-energy tensor in this model
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c
c constant density star
c
elseif (decoded_exact_model .eq. EXACT__constant_density_star) then
rr = sqrt(x(i,j,k)*x(i,j,k)+y(i,j,k)*y(i,j,k)+
& z(i,j,k)*z(i,j,k))
star_m = constant_density_star___mass
star_r = constant_density_star___radius
r3 = star_r**3
if (rr.le.star_r) then
unu = 3.0D0*sqrt(1.0D0-2.0D0*star_m/star_r)
doi = sqrt(1.0D0-2.0D0*star_m*rr*rr/r3)
trei= star_m*(unu-3.0D0*doi)/(2*pi*(unu-doi)*r3)
Ttt = Ttt + 3.0D0*star_m*
& (5.0D0-9.0D0*star_m/star_r - unu*doi
& -star_m*rr*rr/r3)/(8.0D0*pi*r3)
Txx = Txx -trei*(1.0D0+2.0D0*star_m*x(i,j,k)*x(i,j,k)/
& (doi*doi*r3))/2.0D0
Tyy = Tyy -trei*(1.0D0+2.0D0*star_m*y(i,j,k)*y(i,j,k)/
& (doi*doi*r3))/2.0D0
Tzz = Tzz -trei*(1.0D0+2.0D0*star_m*z(i,j,k)*z(i,j,k)/
& (doi*doi*r3))/2.0D0
Txy = Txy -trei*star_m*x(i,j,k)*y(i,j,k)/(doi*doi*r3)
Tyz = Tyz -trei*star_m*y(i,j,k)*z(i,j,k)/(doi*doi*r3)
Txz = Txz -trei*star_m*x(i,j,k)*z(i,j,k)/(doi*doi*r3)
endif
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
else
call CCTK_WARN(0,"Unknown value of Exact::decoded_exact_model")
endif
|
