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/*@@
@file ADMConstraints.F
@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 j_i
@enddesc
@version $Header$
@@*/
#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Arguments.h"
#include "cctk_DefineThorn.h"
#include "CactusEinstein/Einstein/src/Einstein.h"
#ifdef BETATHORNS_CARTOON2D
#include "BetaThorns/Cartoon2D/src/Cartoon2D_tensors.h"
#endif
subroutine ADMConstraints(CCTK_ARGUMENTS)
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
DECLARE_CCTK_FUNCTIONS
integer :: i,j,k
integer :: nx,ny,nz
#ifdef EXCISION_LEGOEXCISION
CCTK_REAL, allocatable, dimension (:,:,:) :: dirx,diry,dirz,aux
#endif
c Stencil width used for calculating constraints
c (for outer boundary condition)
integer, dimension(3),parameter :: sw = 1
c Return code from Cactus sync routine and 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
CCTK_REAL :: det,uxx,uyy,uzz,uxy,uxz,uyz
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"
#include "CactusEinstein/Einstein/src/macro/DETG_declare.h"
#include "CactusEinstein/Einstein/src/macro/UPPERMET_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 This may be needed for CalcTmunu
#include "CactusEinstein/Einstein/src/macro/DETG_guts.h"
det = DETG_DETCG
#include "CactusEinstein/Einstein/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.
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)*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
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/DETG_undefine.h"
#include "CactusEinstein/Einstein/src/macro/UPPERMET_undefine.h"
#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 LegoExcision (must be done before symmetries are applied).
if (excise==1) then
#ifdef EXCISION_LEGOEXCISION
allocate(dirx(nx,ny,nz),diry(nx,ny,nz),dirz(nx,ny,nz))
allocate(aux(nx,ny,nz))
aux = 0.0D0
call excision_findboundary(ierr,emask,nx,ny,nz)
call CCTK_SyncGroup(ierr,cctkGH,"einstein::mask")
call CartSymGN(ierr,cctkGH,"einstein::mask")
call excision_findnormals(ierr,emask,dirx,diry,dirz,nx,ny,nz)
call excision_extrapolate(ierr,ham ,aux,emask,
. dirx,diry,dirz,nx,ny,nz,0.0D0)
call excision_extrapolate(ierr,momx,aux,emask,
. dirx,diry,dirz,nx,ny,nz,0.0D0)
call excision_extrapolate(ierr,momy,aux,emask,
. dirx,diry,dirz,nx,ny,nz,0.0D0)
call excision_extrapolate(ierr,momz,aux,emask,
. dirx,diry,dirz,nx,ny,nz,0.0D0)
deallocate(dirx,diry,dirz)
#else
call CCTK_WARN(0,"You have not compiled with LegoExcision")
#endif
end if
c Apply symmetry boundary conditions.
call CartSymGN(ierr,cctkGH,"admconstraints::hamiltonian")
call CartSymGN(ierr,cctkGH,"admconstraints::momentum")
c Apply flat boundary conditions at outer boundaries.
if (CCTK_Equals(bound,"flat") == 1) then
call BndFlatGN(ierr,cctkGH,sw,"admconstraints::hamiltonian")
call BndFlatGN(ierr,cctkGH,sw,"admconstraints::momentum")
end if
c Synchronize.
if (constraint_communication.eq.1) then
call CCTK_SyncGroup(ierr,cctkGH,"admconstraints::hamiltonian")
call CCTK_SyncGroup(ierr,cctkGH,"admconstraints::momentum")
end if
c Cartoon.
if (cartoon==1) then
#ifdef BETATHORNS_CARTOON2D
call BndCartoon2DGN(ierr,cctkGH,TENSORTYPE_SCALAR,"admconstraints::hamiltonian")
call BndCartoon2DGN(ierr,cctkGH,TENSORTYPE_U,"admconstraints::momentum")
#else
call CCTK_WARN(0,"You have not compiled with Cartoon2D")
#endif
end if
c End
end subroutine ADMConstraints
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