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#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Arguments.h"
#include "cctk_Functions.h"
#include "SpaceMask.h"
/*@@
@routine GRHydro_DiffRho
@date Fri Feb 18 10:02:31 2005
@author Ian Hawke
@desc
Compute first differences in rho
@enddesc
@calls
@calledby
@history
@endhistory
@@*/
subroutine GRHydro_DiffRho(CCTK_ARGUMENTS)
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
DECLARE_CCTK_FUNCTIONS
CCTK_INT :: i, j, k, nx, ny, nz
CCTK_REAL :: idx, idy, idz
CCTK_REAL :: dr_eps = 1.d-2
nx = cctk_lsh(1)
ny = cctk_lsh(2)
nz = cctk_lsh(3)
!!$ idx = 1.d0 / CCTK_DELTA_SPACE(1)
!!$ idy = 1.d0 / CCTK_DELTA_SPACE(2)
!!$ idz = 1.d0 / CCTK_DELTA_SPACE(3)
idx = 1.d0
idy = 1.d0
idz = 1.d0
DiffRho = 0.d0
if (CCTK_EQUALS(gradient_method, "First diff")) then
!!$ Simple first differences
do k = 2, nz - 1
do j = 2, ny - 1
do i = 2, nx - 1
DiffRho(i,j,k) = 0.5d0 * ( &
idx * abs(rho(i+1,j,k) - rho(i-1,j,k)) + &
idy * abs(rho(i,j+1,k) - rho(i,j-1,k)) + &
idz * abs(rho(i,j,k+1) - rho(i,j,k-1)) ) / &
rho(i,j,k)
end do
end do
end do
else if (CCTK_EQUALS(gradient_method, "Curvature")) then
do k = 2, nz - 1
do j = 2, ny - 1
do i = 2, nx - 1
!!$ Gradient as in Paramesh / Flash
DiffRho(i,j,k) = &
sqrt ( &
!!$ xx
(abs(rho(i+1,j,k) - 2.d0 * rho(i,j,k) + rho(i-1,j,k)) / &
( abs(rho(i+1,j,k) - rho(i,j,k)) + &
abs(rho(i,j,k) - rho(i-1,j,k)) + &
dr_eps * (abs(rho(i+1,j,k)) + 2.d0 * abs(rho(i,j,k)) + &
abs(rho(i-1,j,k))) ))**2 + &
!!$ xy
(abs(rho(i+1,j+1,k) - rho(i+1,j-1,k) - &
rho(i-1,j+1,k) + rho(i-1,j-1,k)) / &
( abs(rho(i+1,j,k) - rho(i,j,k)) + &
abs(rho(i,j,k) - rho(i-1,j,k)) + &
dr_eps * (abs(rho(i+1,j+1,k)) + abs(rho(i+1,j-1,k)) + &
abs(rho(i-1,j+1,k)) + abs(rho(i-1,j-1,k))) ))**2 + &
!!$ xz
(abs(rho(i+1,j,k+1) - rho(i+1,j,k-1) - &
rho(i-1,j,k+1) + rho(i-1,j,k-1)) / &
( abs(rho(i+1,j,k) - rho(i,j,k)) + &
abs(rho(i,j,k) - rho(i-1,j,k)) + &
dr_eps * (abs(rho(i+1,j,k+1)) + abs(rho(i+1,j,k-1)) + &
abs(rho(i-1,j,k+1)) + abs(rho(i-1,j,k-1))) ))**2 + &
!!$ yx
(abs(rho(i+1,j+1,k) - rho(i+1,j-1,k) - &
rho(i-1,j+1,k) + rho(i-1,j-1,k)) / &
( abs(rho(i,j+1,k) - rho(i,j,k)) + &
abs(rho(i,j,k) - rho(i,j-1,k)) + &
dr_eps * (abs(rho(i+1,j+1,k)) + abs(rho(i+1,j-1,k)) + &
abs(rho(i-1,j+1,k)) + abs(rho(i-1,j-1,k))) ))**2 + &
!!$ yy
(abs(rho(i,j+1,k) - 2.d0 * rho(i,j,k) + rho(i,j-1,k)) / &
( abs(rho(i,j+1,k) - rho(i,j,k)) + &
abs(rho(i,j,k) - rho(i,j-1,k)) + &
dr_eps * (abs(rho(i,j+1,k)) + 2.d0 * abs(rho(i,j,k)) + &
abs(rho(i,j-1,k))) ))**2 + &
!!$ yz
(abs(rho(i,j+1,k+1) - rho(i,j+1,k-1) - &
rho(i,j-1,k+1) + rho(i,j-1,k-1)) / &
( abs(rho(i,j+1,k) - rho(i,j,k)) + &
abs(rho(i,j,k) - rho(i,j-1,k)) + &
dr_eps * (abs(rho(i,j+1,k+1)) + abs(rho(i,j+1,k-1)) + &
abs(rho(i,j-1,k+1)) + abs(rho(i,j-1,k-1))) ))**2 + &
!!$ zx
(abs(rho(i+1,j,k+1) - rho(i+1,j,k-1) - &
rho(i-1,j,k+1) + rho(i-1,j,k-1)) / &
( abs(rho(i,j,k+1) - rho(i,j,k)) + &
abs(rho(i,j,k) - rho(i,j,k-1)) + &
dr_eps * (abs(rho(i+1,j,k+1)) + abs(rho(i+1,j,k-1)) + &
abs(rho(i-1,j,k+1)) + abs(rho(i-1,j,k-1))) ))**2 + &
!!$ zy
(abs(rho(i,j+1,k+1) - rho(i,j-1,k+1) - &
rho(i,j+1,k-1) + rho(i,j-1,k-1)) / &
( abs(rho(i,j,k+1) - rho(i,j,k)) + &
abs(rho(i,j,k) - rho(i,j,k-1)) + &
dr_eps * (abs(rho(i,j+1,k+1)) + abs(rho(i,j-1,k+1)) + &
abs(rho(i,j+1,k-1)) + abs(rho(i,j-1,k-1))) ))**2 + &
!!$ zz
(abs(rho(i,j,k+1) - 2.d0 * rho(i,j,k) + rho(i,j,k-1)) / &
( abs(rho(i,j,k+1) - rho(i,j,k)) + &
abs(rho(i,j,k) - rho(i,j,k-1)) + &
dr_eps * (abs(rho(i,j,k+1)) + 2.d0 * abs(rho(i,j,k)) + &
abs(rho(i,j,k-1))) ))**2 &
)
end do
end do
end do
else if (CCTK_EQUALS(gradient_method, "Rho weighted")) then
DiffRho = &
rho*(CCTK_DELTA_SPACE(1)*CCTK_DELTA_SPACE(2)*CCTK_DELTA_SPACE(3))**2
else
call CCTK_WARN(0, "Value of gradient_method not recognized")
end if
end subroutine GRHydro_DiffRho
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