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cc/*@@
c @file ADMConstraints.F
c @date Aug 98
c @desc
c Calculate the ADM Constraints for output:
c
c Hamiltonian Constraint is:
c
c R - K^i_j K^j_i + trK^2 - 16 Pi rho
c
c Momentum Constraints are:
c
c Del_j K_i^j - Del_i trK - 8 Pi j_i
c
c @enddesc
c@@*/
#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Arguments.h"
#include "CactusEinstein/Einstein/src/Einstein.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, dimension(3),parameter :: sw = 1
c Return code from Cactus boundary conditions.
integer ierr
c Various real variables.
CCTK_REAL :: dx,dy,dz
CCTK_REAL :: m_rho,m_sx,m_sy,m_sz
CCTK_REAL :: pi,ialp,ialp2
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 "CactusEinstein/Einstein/src/macro/HAMADM_declare.h"
#include "CactusEinstein/Einstein/src/macro/MOMXADM_declare.h"
#include "CactusEinstein/Einstein/src/macro/MOMYADM_declare.h"
#include "CactusEinstein/Einstein/src/macro/MOMZADM_declare.h"
c --------------------------------------------------------------
c Grid parameters.
dx = cctk_delta_space(1)
dy = cctk_delta_space(2)
dz = cctk_delta_space(3)
nx = cctk_lsh(1)
ny = cctk_lsh(2)
nz = cctk_lsh(3)
c Fill with zeros.
ham = 0.0D0
momx = 0.0D0
momy = 0.0D0
momz = 0.0D0
c Calculate constraints.
pi = acos(-1.0D0)
do k=2,nz-1
do j=2,ny-1
do i=2,nx-1
ialp = 1.0D0/alp(i,j,k)
ialp2 = ialp**2
c Calculate the stress energy tensor at this point
c ------------------------------------------------
c Initialize stress-energy tensor components.
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"
c Calculate the hamiltonian constraint
c ------------------------------------
c Geometric piece.
#include "CactusEinstein/Einstein/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 == SHIFT_ACTIVE) 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)**2*Ttx
& + betay(i,j,k)**2*Tty
& + betaz(i,j,k)**2*Ttz)*2.0D0)
end if
ham(i,j,k) = HAMADM_HAMADM - 16.0D0*pi*m_rho
c Calculate the Momentum constraints
c ----------------------------------
c Geometric piece.
#include "CactusEinstein/Einstein/src/macro/MOMXADM_guts.h"
#include "CactusEinstein/Einstein/src/macro/MOMYADM_guts.h"
#include "CactusEinstein/Einstein/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 == SHIFT_ACTIVE) 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
end do
end do
end do
#include "CactusEinstein/Einstein/src/macro/HAMADM_undefine.h"
#include "CactusEinstein/Einstein/src/macro/MOMXADM_undefine.h"
#include "CactusEinstein/Einstein/src/macro/MOMYADM_undefine.h"
#include "CactusEinstein/Einstein/src/macro/MOMZADM_undefine.h"
c Apply symmetry boundary conditions.
call CartSymGN(ierr,cctkGH,"admconstraints::admconstraints")
c Apply flat boundary conditions at outer boundaries.
if (CCTK_Equals(bound,"flat") == 1) then
call BndFlatGN(ierr,cctkGH,sw,"admconstraints::admconstraints")
end if
c Synchronize.
if (constraint_communication.eq.1) then
call CCTK_SyncGroup(cctkGH,"admconstraints::admconstraints")
end if
c End
end subroutine ADMConstraints
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