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/*@@
@file ADMConstraints.F77
@date August 98
@desc
Calculate the ADM Constraints for output:
Hamiltonian Constraint is:
H = R - K^i_j K^j_i + trK^2 - 16 Pi rho
Momentum Constraints are:
M_i = Del_j K_i^j - Del_i trK - 8 Pi S_i
@enddesc
@version $Header$
@@*/
#include "cctk.h"
#include "cctk_Arguments.h"
#include "cctk_Functions.h"
#include "cctk_Parameters.h"
#include "SpaceMask.h"
subroutine ADMConstraints(CCTK_ARGUMENTS)
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
DECLARE_CCTK_FUNCTIONS
integer i,j,k
integer nx,ny,nz
c Stencil width used for calculating constraints
c (for outer boundary condition)
integer sw(3)
logical docalc
c flags for excision
integer ex_field, ex_type_excised
c Various real variables.
CCTK_REAL m_rho,m_sx,m_sy,m_sz
CCTK_REAL pi,ialp,ialp2
CCTK_REAL det,uxx,uyy,uzz,uxy,uxz,uyz
#include "EinsteinBase/ADMMacros/src/macro/ADM_Spacing_declare.h"
c Temporaries for the Stress-Energy tensor.
CCTK_REAL Ttt,Ttx,Tty,Ttz,Txx,Txy,Txz,Tyy,Tyz,Tzz
c Matter declarations.
#include "CalcTmunu_temps.inc"
c Macros from Standard Einstein.
#include "EinsteinBase/ADMMacros/src/macro/HAMADM_declare.h"
#include "EinsteinBase/ADMMacros/src/macro/MOMXADM_declare.h"
#include "EinsteinBase/ADMMacros/src/macro/MOMYADM_declare.h"
#include "EinsteinBase/ADMMacros/src/macro/MOMZADM_declare.h"
#include "EinsteinBase/ADMMacros/src/macro/DETG_declare.h"
#include "EinsteinBase/ADMMacros/src/macro/UPPERMET_declare.h"
c --------------------------------------------------------------
if (check_excision_bitmask .ne. 0) then
call SpaceMask_GetTypeBits(ex_field, excision_mask_name)
call SpaceMask_GetStateBits(ex_type_excised, excision_mask_name, \
excision_type_excised)
end if
sw(1) = 1
sw(2) = 1
sw(3) = 1
c Grid parameters.
#include "EinsteinBase/ADMMacros/src/macro/ADM_Spacing.h"
nx = cctk_lsh(1)
ny = cctk_lsh(2)
nz = cctk_lsh(3)
c Fill with zeros.
do k=1,nz
do j=1,ny
do i=1,nx
ham(i,j,k) = 0.0D0
hamnormalized(i,j,k) = 0.0D0
momx(i,j,k) = 0.0D0
momy(i,j,k) = 0.0D0
momz(i,j,k) = 0.0D0
end do
end do
end do
c Calculate constraints.
pi = acos(-1.0D0)
do k=2,nz-1
do j=2,ny-1
do i=2,nx-1
if ( (i<3).or.(i>cctk_lsh(1)-2).or.
. (j<3).or.(j>cctk_lsh(2)-2).or.
. (k<3).or.(k>cctk_lsh(3)-2) ) then
local_spatial_order = 2
else
local_spatial_order = spatial_order
end if
docalc = .TRUE.
if (use_mask .eq. 1) then
if (abs(emask(i,j,k)-1) > 0.001) then
docalc = .FALSE.
elseif (check_excision_bitmask .ne. 0) then
if (SpaceMask_CheckStateBitsF90(space_mask, i, j, k,\
ex_field, ex_type_excised)) then
docalc = .FALSE.
end if
end if
end if
if (docalc) then
ialp = 1.0D0/alp(i,j,k)
ialp2 = ialp**2
c Calculate the stress energy tensor at this point
c ------------------------------------------------
c This may be needed for CalcTmunu
#include "EinsteinBase/ADMMacros/src/macro/DETG_guts.h"
det = DETG_DETCG
#include "EinsteinBase/ADMMacros/src/macro/UPPERMET_guts.h"
uxx = UPPERMET_UXX; uxy = UPPERMET_UXY; uxz = UPPERMET_UXZ
uyy = UPPERMET_UYY; uyz = UPPERMET_UYZ; uzz = UPPERMET_UZZ
c Initialize stress-energy tensor components.
if (stress_energy_state .ne. 0) then
Ttt = eTtt(i,j,k)
Ttx = eTtx(i,j,k); Tty = eTty(i,j,k); Ttz = eTtz(i,j,k)
Txx = eTxx(i,j,k); Tyy = eTyy(i,j,k); Tzz = eTzz(i,j,k)
Txy = eTxy(i,j,k); Txz = eTxz(i,j,k); Tyz = eTyz(i,j,k)
else
Ttt = 0.0D0
Ttx = 0.0D0; Tty = 0.0D0; Ttz = 0.0D0
Txx = 0.0D0; Tyy = 0.0D0; Tzz = 0.0D0
Txy = 0.0D0; Txz = 0.0D0; Tyz = 0.0D0
c Include macro for stress energy tensor.
#include "CalcTmunu.inc"
end if
c Calculate the hamiltonian constraint
c ------------------------------------
c Geometric piece.
#include "EinsteinBase/ADMMacros/src/macro/HAMADM_guts.h"
c Add matter terms: - 16*pi*rho
c
c with rho defined as:
c
c rho = n_a n_b T^{ab} = n^a n^b T_{ab}
c = (T_00 - 2 beta^i T_{i0} + beta^i beta^j T_{ij})/alpha^2
m_rho = ialp2*Ttt
if (shift_state .eq. 1) then
m_rho = m_rho + ialp2
& *(betax(i,j,k)**2*Txx
& + betay(i,j,k)**2*Tyy
& + betaz(i,j,k)**2*Tzz
& +(betax(i,j,k)*betay(i,j,k)*Txy
& + betax(i,j,k)*betaz(i,j,k)*Txz
& + betay(i,j,k)*betaz(i,j,k)*Tyz)*2.0D0
& -(betax(i,j,k)*Ttx
& + betay(i,j,k)*Tty
& + betaz(i,j,k)*Ttz)*2.0D0)
end if
ham(i,j,k) = HAMADM_HAMADM - 16.0D0*pi*m_rho
if ((HAMADM_HAMADMABS + abs(16.0D0*pi*m_rho))==0) then
hamnormalized(i,j,k) = abs(ham(i,j,k))
else
hamnormalized(i,j,k) = abs(ham(i,j,k))/
& (HAMADM_HAMADMABS + abs(16.0D0*pi*m_rho))
end if
c Calculate the Momentum constraints
c ----------------------------------
c Geometric piece.
#include "EinsteinBase/ADMMacros/src/macro/MOMXADM_guts.h"
#include "EinsteinBase/ADMMacros/src/macro/MOMYADM_guts.h"
#include "EinsteinBase/ADMMacros/src/macro/MOMZADM_guts.h"
c Add matter terms: - 8*pi*S_i
c
c with S_i defined as:
c
c S_i = - g_{ia} n_b T^{ab} = - g_i^a n^b T_{ab}
c = - (T_{i0} - beta^j T_{ij})/alpha
m_sx = - ialp*Ttx
m_sy = - ialp*Tty
m_sz = - ialp*Ttz
if (shift_state .eq. 1) then
m_sx = m_sx + ialp
& *(betax(i,j,k)*Txx
& + betay(i,j,k)*Txy
& + betaz(i,j,k)*Txz)
m_sy = m_sy + ialp
& *(betax(i,j,k)*Txy
& + betay(i,j,k)*Tyy
& + betaz(i,j,k)*Tyz)
m_sz = m_sz + ialp
& *(betax(i,j,k)*Txz
& + betay(i,j,k)*Tyz
& + betaz(i,j,k)*Tzz)
end if
momx(i,j,k) = MOMXADM_MOMXADM - 8.0D0*pi*m_sx
momy(i,j,k) = MOMYADM_MOMYADM - 8.0D0*pi*m_sy
momz(i,j,k) = MOMZADM_MOMZADM - 8.0D0*pi*m_sz
else
ham(i,j,k) = excised_value
momx(i,j,k) = excised_value
momy(i,j,k) = excised_value
momz(i,j,k) = excised_value
end if
end do
end do
end do
#include "EinsteinBase/ADMMacros/src/macro/DETG_undefine.h"
#include "EinsteinBase/ADMMacros/src/macro/UPPERMET_undefine.h"
#include "EinsteinBase/ADMMacros/src/macro/HAMADM_undefine.h"
#include "EinsteinBase/ADMMacros/src/macro/MOMXADM_undefine.h"
#include "EinsteinBase/ADMMacros/src/macro/MOMYADM_undefine.h"
#include "EinsteinBase/ADMMacros/src/macro/MOMZADM_undefine.h"
return
end
subroutine ADMConstraints_Boundaries(CCTK_ARGUMENTS)
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
DECLARE_CCTK_FUNCTIONS
CCTK_INT, parameter :: izero = 0
integer, parameter :: ik = kind (izero)
c Return code from Cactus sync routine and boundary conditions.
integer ierr
c Apply flat boundary conditions at outer boundaries.
if (CCTK_EQUALS(bound,"flat")) then
ierr = Boundary_SelectGroupForBC(cctkGH, int(CCTK_ALL_FACES,ik), 1_ik, -1_ik,
$ "admconstraints::hamiltonian", "Flat")
ierr = Boundary_SelectGroupForBC(cctkGH, int(CCTK_ALL_FACES,ik), 1_ik, -1_ik,
$ "admconstraints::normalized_hamiltonian", "Flat")
ierr = Boundary_SelectGroupForBC(cctkGH, int(CCTK_ALL_FACES,ik), 1_ik, -1_ik,
$ "admconstraints::momentum", "Flat")
else
ierr = Boundary_SelectGroupForBC(cctkGH, int(CCTK_ALL_FACES,ik), 1_ik, -1_ik,
$ "admconstraints::hamiltonian", "None")
ierr = Boundary_SelectGroupForBC(cctkGH, int(CCTK_ALL_FACES,ik), 1_ik, -1_ik,
$ "admconstraints::normalized_hamiltonian", "None")
ierr = Boundary_SelectGroupForBC(cctkGH, int(CCTK_ALL_FACES,ik), 1_ik, -1_ik,
$ "admconstraints::momentum", "None")
end if
return
end
|
