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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"
subroutine EHFinder_Sources(CCTK_ARGUMENTS)
use EHFinder_mod
implicit none
DECLARE_CCTK_PARAMETERS
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_FUNCTIONS
CCTK_INT :: i, j, k
CCTK_REAL :: idx, idy, idz, mdelta
CCTK_REAL :: a, b, c
CCTK_REAL :: g4tt, g4tx, g4ty, g4tz, g4xx, g4xy, g4xz, g4yy, g4yz, g4zz
CCTK_REAL :: g3xx, g3xy, g3xz, g3yy, g3yz, g3zz
CCTK_REAL :: gxxc, gxyc, gxzc, gyyc, gyzc, gzzc, psito4
CCTK_REAL :: idetg, alp2, tmp1, tmp2, tmp3
CCTK_REAL :: ratio, cfactor
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
! calculate 1/(2*delta) in each direction
#include "include/physical_part.h"
idx = half / cctk_delta_space(1)
idy = half / cctk_delta_space(2)
idz = half / cctk_delta_space(3)
mdelta = maxval ( cctk_delta_space )
if ( CCTK_EQUALS ( upwind_type, 'intrinsic' ) ) then
do k = kzl, kzr
do j = jyl, jyr
do i = ixl, ixr
if ( f(i,j,k) .gt. fmin_bound - three*mdelta ) then
#include "include/centered_second2.h"
else
#include "include/upwind_second2.h"
end if
end do
end do
end do
end if
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 ( CCTK_EQUALS ( upwind_type, 'characteristic' ) ) then
do k = kzl, kzr
do j = jyl, jyr
do i = ixl, ixr
#include "include/metric.h"
#include "include/upwind_characteristic_second2.h"
end do
end do
end do
end if
if ( CCTK_EQUALS ( metric_type, 'physical' ) ) then
do k = kzl, kzr
do j = jyl, jyr
do i = ixl, ixr
if ( eh_mask(i,j,k) .ge. 0 ) then
alp2 = alp(i,j,k)**2
g4tt = -one
g4tx = betax(i,j,k)
g4ty = betay(i,j,k)
g4tz = betaz(i,j,k)
tmp1 = gyy(i,j,k)*gzz(i,j,k) - gyz(i,j,k)**2
tmp2 = gxz(i,j,k)*gyz(i,j,k) - gxy(i,j,k)*gzz(i,j,k)
tmp3 = gxy(i,j,k)*gyz(i,j,k) - gxz(i,j,k)*gyy(i,j,k)
idetg = one / ( gxx(i,j,k)*tmp1 + gxy(i,j,k)*tmp2 + gxz(i,j,k)*tmp3 )
g4xx = tmp1 * idetg
g4xy = tmp2 * idetg
g4xz = tmp3 * idetg
g4yy = ( gxx(i,j,k)*gzz(i,j,k) - gxz(i,j,k)**2 ) * idetg
g4yz = ( gxy(i,j,k)*gxz(i,j,k) - gxx(i,j,k)*gyz(i,j,k) ) * idetg
g4zz = ( gxx(i,j,k)*gyy(i,j,k) - gxy(i,j,k)**2 ) * idetg
g4xx = alp2*g4xx - betax(i,j,k)**2
g4xy = alp2*g4xy - betax(i,j,k)*betay(i,j,k)
g4xz = alp2*g4xz - betax(i,j,k)*betaz(i,j,k)
g4yy = alp2*g4yy - betay(i,j,k)**2
g4yz = alp2*g4yz - betay(i,j,k)*betaz(i,j,k)
g4zz = alp2*g4zz - betaz(i,j,k)**2
a = g4tt
b = two * ( g4tx * dfx(i,j,k) + &
g4ty * dfy(i,j,k) + &
g4tz * dfz(i,j,k) )
c = g4xx * dfx(i,j,k)**2 + &
g4yy * dfy(i,j,k)**2 + &
g4zz * dfz(i,j,k)**2 + &
two * ( g4xy * dfx(i,j,k) * dfy(i,j,k) + &
g4xz * dfx(i,j,k) * dfz(i,j,k) + &
g4yz * dfy(i,j,k) * dfz(i,j,k) )
if ( b .lt. zero ) then
sf(i,j,k) = ( -b + sqrt(b**2 - four*a*c) ) / ( two*a )
else
sf(i,j,k) = two*c / ( -b - sqrt(b**2 - 4*a*c) )
end if
else
sf(i,j,k) = zero
end if
end do
end do
end do
end if
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) .ge. 0 ) then
alp2 = alp(i,j,k)**2
g4tt = -one
g4tx = betax(i,j,k)
g4ty = betay(i,j,k)
g4tz = betaz(i,j,k)
psito4 = psi(i,j,k)**4
gxxc = gxx(i,j,k) * psito4
gxyc = gxy(i,j,k) * psito4
gxzc = gxz(i,j,k) * psito4
gyyc = gyy(i,j,k) * psito4
gyzc = gyz(i,j,k) * psito4
gzzc = gzz(i,j,k) * psito4
tmp1 = gyyc*gzzc - gyzc**2
tmp2 = gxzc*gyzc - gxyc*gzzc
tmp3 = gxyc*gyzc - gxzc*gyyc
idetg = one / ( gxxc*tmp1 + gxyc*tmp2 + gxzc*tmp3 )
g4xx = tmp1 * idetg
g4xy = tmp2 * idetg
g4xz = tmp3 * idetg
g4yy = ( gxxc*gzzc - gxzc**2 ) * idetg
g4yz = ( gxyc*gxzc - gxxc*gyzc ) * idetg
g4zz = ( gxxc*gyyc - gxyc**2 ) * idetg
g4xx = alp2*g4xx - betax(i,j,k)**2
g4xy = alp2*g4xy - betax(i,j,k)*betay(i,j,k)
g4xz = alp2*g4xz - betax(i,j,k)*betaz(i,j,k)
g4yy = alp2*g4yy - betay(i,j,k)**2
g4yz = alp2*g4yz - betay(i,j,k)*betaz(i,j,k)
g4zz = alp2*g4zz - betaz(i,j,k)**2
a = g4tt
b = two * ( g4tx * dfx(i,j,k) + &
g4ty * dfy(i,j,k) + &
g4tz * dfz(i,j,k) )
c = g4xx * dfx(i,j,k)**2 + &
g4yy * dfy(i,j,k)**2 + &
g4zz * dfz(i,j,k)**2 + &
two * ( g4xy * dfx(i,j,k) * dfy(i,j,k) + &
g4xz * dfx(i,j,k) * dfz(i,j,k) + &
g4yz * dfy(i,j,k) * dfz(i,j,k) )
if ( b .le. zero ) then
sf(i,j,k) = ( -b + sqrt(b**2 - four*a*c) ) / ( two*a )
else
sf(i,j,k) = two*c / ( -b - sqrt(b**2 - 4*a*c) )
end if
sf(i,j,k) = sf(i,j,k)*sign(one,alp(i,j,k))
! if ( i .eq. 41 .and. j .eq. 20 .and. k .eq. 25 ) then
! print*,i,j,k
! print*,f(i,j,k),eh_mask(i,j,k)
! print*,f(i-1,j,k),f(i+1,j,k),eh_mask(i-1,j,k),eh_mask(i+1,j,k)
! print*,f(i,j-1,k),f(i,j+1,k),eh_mask(i,j-1,k),eh_mask(i,j+1,k)
! print*,f(i,j,k-1),f(i,j,k+1),eh_mask(i,j,k-1),eh_mask(i,j,k+1)
! print*,dfx(i,j,k),dfy(i,j,k),dfz(i,j,k)
! print*
! print*,x(i,j,k),y(i,j,k),z(i,j,k)
! print*,alp(i,j,k)
! print*,betax(i,j,k),betay(i,j,k),betaz(i,j,k)
! print*,gxx(i,j,k),gxy(i,j,k),gxz(i,j,k)
! print*,gyy(i,j,k),gyz(i,j,k),gzz(i,j,k)
! print*,psi(i,j,k)
! print*
! print*,tmp1,tmp2,tmp3
! print*,gxxc*tmp1 + gxyc*tmp2 + gxzc*tmp3
! print*,idetg
! print*
! print*,g4xx,g4xy,g4xz
! print*,g4yy,g4yz,g4zz
! print*
! print*,a,b,c
! print*,sf(i,j,k)
! print*
! print*
! end if
else
sf(i,j,k) = zero
end if
end do
end do
end do
end if
return
end subroutine EHFinder_Sources
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