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! Calculation of the sources for the level set function.
! $Header$
#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Arguments.h"
#include "cctk_Functions.h"
subroutine EHFinder_Sources(CCTK_ARGUMENTS)
use EHFinder_mod
implicit none
DECLARE_CCTK_PARAMETERS
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_FUNCTIONS
CCTK_INT :: i, j, k, l
CCTK_REAL :: idx, idy, idz
CCTK_REAL :: a, b, c
CCTK_REAL :: gxxc, gxyc, gxzc, gyyc, gyzc, gzzc, psito4
CCTK_REAL :: idetg, alp2, tmp1, tmp2, tmp3
CCTK_REAL :: ratio, cfactor, ssign
CCTK_REAL, dimension(3) :: maxpos, cdx, dfup
CCTK_REAL :: al, ar, bl, br, cl, cr
CCTK_REAL :: alminus, alplus, blminus, blplus, clminus, clplus
CCTK_REAL :: arminus, arplus, brminus, brplus, crminus, crplus
#include "include/physical_part.h"
! calculate 1/(2*delta) in each direction
idx = half / CCTK_DELTA_SPACE(1)
idy = half / CCTK_DELTA_SPACE(2)
idz = half / CCTK_DELTA_SPACE(3)
! Set the sign depending on the surface direction.
if ( CCTK_EQUALS ( surface_direction, 'outward' ) ) ssign = one
if ( CCTK_EQUALS ( surface_direction, 'inward' ) ) ssign = -one
do l = 1, eh_number_level_sets
do k = kzl, kzr
do j = jyl, jyr
do i = ixl, ixr
! Calculate the inverse of the 3-metric
# include "include/metric.h"
end do
end do
end do
! Calculate the derivatives of the level set function using the intrinsic
! scheme. Note, this should never be used and may disappear in later versions.
if ( CCTK_EQUALS ( upwind_type, 'intrinsic' ) ) then
do k = kzl, kzr
do j = jyl, jyr
do i = ixl, ixr
#include "include/upwind_second2.h"
end do
end do
end do
end if
! Calculate the derivatives of the level set function using shift upwinding.
if ( CCTK_EQUALS ( upwind_type, 'shift' ) ) then
do k = kzl, kzr
do j = jyl, jyr
do i = ixl, ixr
#include "include/upwind_shift_second2.h"
end do
end do
end do
end if
! If the three metric is the static conformal metric we convert the inverse
! three metric to the physical inverse three metric by multiplying with
! psi^(-4).
if ( CCTK_EQUALS ( metric_type, 'static conformal' ) ) then
do k = kzl, kzr
do j = jyl,jyr
do i = ixl, ixr
if ( eh_mask(i,j,k,l) .ge. 0 ) then
psito4 = psi(i,j,k)**(-4)
g3xx(i,j,k) = g3xx(i,j,k) * psito4
g3xy(i,j,k) = g3xy(i,j,k) * psito4
g3xz(i,j,k) = g3xz(i,j,k) * psito4
g3yy(i,j,k) = g3yy(i,j,k) * psito4
g3yz(i,j,k) = g3yz(i,j,k) * psito4
g3zz(i,j,k) = g3zz(i,j,k) * psito4
end if
end do
end do
end do
end if
! Calculate the derivatives of the level set using characteristic upwinding.
if ( CCTK_EQUALS ( upwind_type, 'characteristic' ) ) then
do k = kzl, kzr
do j = jyl, jyr
do i = ixl, ixr
! We use centered derivatives to figure out which direction
! to upwind in.
#include "include/upwind_characteristic_second2.h"
end do
end do
end do
end if
do k = kzl, kzr
do j = jyl, jyr
do i = ixl, ixr
! If the current point is active ...
if ( eh_mask(i,j,k,l) .ge. 0 ) then
! Square the lapse.
alp2 = alp(i,j,k)**2
! Calculate beta^i df_i.
tmp1 = betax(i,j,k) * dfx(i,j,k,l) + &
betay(i,j,k) * dfy(i,j,k,l) + &
betaz(i,j,k) * dfz(i,j,k,l)
! Calculate gamma^ij df_i df_j.
tmp2 = g3xx(i,j,k) * dfx(i,j,k,l)**2 + &
g3yy(i,j,k) * dfy(i,j,k,l)**2 + &
g3zz(i,j,k) * dfz(i,j,k,l)**2 + &
two * ( g3xy(i,j,k) * dfx(i,j,k,l) * dfy(i,j,k,l) + &
g3xz(i,j,k) * dfx(i,j,k,l) * dfz(i,j,k,l) + &
g3yz(i,j,k) * dfy(i,j,k,l) * dfz(i,j,k,l) )
! If the metric is positive definite ...
if ( tmp2 .ge. zero ) then
! Calculate the right hand side.
sf(i,j,k,l) = tmp1 - ssign * sqrt ( alp2 * tmp2 )
! If the lapse is negative we change the sign of the right hand
! side function. This is done to be able to handle for example
! Schwarzschild in isotropic coordinates with the isotropic
! lapse.
sf(i,j,k,l) = sf(i,j,k,l) * sign ( one, alp(i,j,k) )
else
! Otherwise print a level 0 warning.
call CCTK_WARN ( 0, '3-metric not positive definite: Stopping' )
end if
else
sf(i,j,k,l) = zero
end if
end do
end do
end do
end do
return
end subroutine EHFinder_Sources
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