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C $Header$
#include "cctk.h"
#include "cctk_Parameters.h"
#include "cctk_Arguments.h"
#include "cctk_Functions.h"
subroutine Exact__xyz_blended_boundary(CCTK_ARGUMENTS)
implicit none
DECLARE_CCTK_ARGUMENTS
DECLARE_CCTK_PARAMETERS
DECLARE_CCTK_FUNCTIONS
logical doKij, doGij, doLapse, doShift
integer i,j,k
integer nx,ny,nz
integer ninterps
CCTK_REAL xblend, yblend, zblend
CCTK_REAL xmin, xmax, ymin, ymax, zmin, zmax
CCTK_REAL xfrac, yfrac, zfrac, onemxfrac, onemyfrac, onemzfrac
CCTK_REAL oonints
CCTK_REAL sfrac, onemsfrac
CCTK_REAL gxxe, gyye, gzze, gxye, gyze, gxze
CCTK_REAL kxxe, kyye, kzze, kxye, kyze, kxze
CCTK_REAL dxgxxe, dxgyye, dxgzze, dxgxye, dxgyze, dxgxze
CCTK_REAL dygxxe, dygyye, dygzze, dygxye, dygyze, dygxze
CCTK_REAL dzgxxe, dzgyye, dzgzze, dzgxye, dzgyze, dzgxze
CCTK_REAL alpe, axe, aye, aze
CCTK_REAL betaxe,betaye,betaze
CCTK_REAL bxxe,bxye,bxze,byxe,byye,byze,bzxe,bzye,bzze
CCTK_REAL det, uxx, uxy, uxz, uyy, uyz, uzz
CCTK_REAL
$ exact_psi,
$ exact_psix, exact_psiy, exact_psiz,
$ exact_psixx, exact_psiyy, exact_psizz,
$ exact_psixy, exact_psiyz, exact_psixz
CCTK_REAL dx,dy,dz,time
integer ierr
C Grid parameters.
nx = cctk_lsh(1)
ny = cctk_lsh(2)
nz = cctk_lsh(3)
dx = cctk_delta_space(1)
dy = cctk_delta_space(2)
dz = cctk_delta_space(3)
time = cctk_time
C Other parameters.
doKij = (exblend_Ks.eq.1)
doGij = (exblend_gs.eq.1)
doLapse = ((exblend_gauge.eq.1).and.
$ (CCTK_Equals(lapse_evolution_method,"exact").ne.0))
doShift = ((exblend_gauge.eq.1).and.
$ (CCTK_Equals(shift_evolution_method,"exact").ne.0))
if (exblend_width.lt.0) then
xblend = - exblend_width*dx
yblend = - exblend_width*dy
zblend = - exblend_width*dz
else
xblend = exblend_width
yblend = exblend_width
zblend = exblend_width
endif
call CCTK_CoordRange(ierr,cctkGH,xmin,xmax,-1,"x","cart3d")
call CCTK_CoordRange(ierr,cctkGH,ymin,ymax,-1,"y","cart3d")
call CCTK_CoordRange(ierr,cctkGH,zmin,zmax,-1,"z","cart3d")
do k=1,nz
do j=1,ny
do i=1,nx
c We only do anything if in the blending region
if (x(i,j,k) .ge. xmax - xblend .or.
$ x(i,j,k) .le. xmin + xblend .or.
$ y(i,j,k) .ge. ymax - yblend .or.
$ y(i,j,k) .le. ymin + yblend .or.
$ z(i,j,k) .ge. zmax - zblend .or.
$ z(i,j,k) .le. zmin + zblend) then
C Initialize the psi of exact
C (also to tell the models about the conformal_state)
if (conformal_state .ne. 0) then
exact_psi = 1.0D0
else
exact_psi = 0.0D0
end if
exact_psix = 0.0D0
exact_psiy = 0.0D0
exact_psiz = 0.0D0
exact_psixx = 0.0D0
exact_psixx = 0.0D0
exact_psizz = 0.0D0
exact_psixy = 0.0D0
exact_psiyz = 0.0D0
exact_psixz = 0.0D0
call Exact__Bona_Masso_data(
$ decoded_exact_model,
$ x(i,j,k), y(i,j,k), z(i,j,k), time,
$ gxxe, gyye, gzze, gxye, gyze, gxze,
$ kxxe, kyye, kzze, kxye, kyze, kxze,
$ exact_psi,
$ exact_psix, exact_psiy, exact_psiz,
$ exact_psixx, exact_psiyy, exact_psizz,
$ exact_psixy, exact_psiyz, exact_psixz,
$ dxgxxe, dxgyye, dxgzze, dxgxye, dxgyze, dxgxze,
$ dygxxe, dygyye, dygzze, dygxye, dygyze, dygxze,
$ dzgxxe, dzgyye, dzgzze, dzgxye, dzgyze, dzgxze,
$ alpe, axe, aye, aze, betaxe, betaye, betaze,
$ bxxe, bxye, bxze, byxe,
$ byye, byze, bzxe, bzye, bzze)
c This sucks, but we want the exact vs so we can blend them also.
det = -(gxze**2*gyye)
& + 2.d0*gxye*gxze*gyze
& - gxxe*gyze**2
& - gxye**2*gzze
& + gxxe*gyye*gzze
uxx=(-gyze**2 + gyye*gzze)/det
uxy=(gxze*gyze - gxye*gzze)/det
uyy=(-gxze**2 + gxxe*gzze)/det
uxz=(-gxze*gyye + gxye*gyze)/det
uyz=(gxye*gxze - gxxe*gyze)/det
uzz=(-gxye**2 + gxxe*gyye)/det
c OK so 6 blending cases. If frac = 1 we get all exact
ninterps = 0
xfrac = 0.0D0
onemxfrac = 0.0D0
yfrac = 0.0D0
onemyfrac = 0.0D0
zfrac = 0.0D0
onemzfrac = 0.0D0
if (x(i,j,k) .le. xmin + xblend) then
xfrac = 1.0D0 - (x(i,j,k)-xmin) / xblend
onemxfrac = 1.0D0 - xfrac
ninterps = ninterps + 1
endif
if (x(i,j,k) .ge. xmax - xblend) then
xfrac = 1.0D0 - (xmax - x(i,j,k)) / xblend
onemxfrac = 1.0D0 - xfrac
ninterps = ninterps + 1
endif
if (y(i,j,k) .le. ymin + yblend) then
yfrac = 1.0D0 - (y(i,j,k)-ymin) / yblend
onemyfrac = 1.0D0 - yfrac
ninterps = ninterps + 1
endif
if (y(i,j,k) .ge. ymax - yblend) then
yfrac = 1.0D0 - (ymax - y(i,j,k)) / yblend
onemyfrac = 1.0D0 - yfrac
ninterps = ninterps + 1
endif
if (z(i,j,k) .le. zmin + zblend) then
zfrac = 1.0D0 - (z(i,j,k)-zmin) / zblend
onemzfrac = 1.0D0 - zfrac
ninterps = ninterps + 1
endif
if (z(i,j,k) .ge. zmax - zblend) then
zfrac = 1.0D0 - (zmax - z(i,j,k)) / zblend
onemzfrac = 1.0D0 - zfrac
ninterps = ninterps + 1
endif
oonints = 1.0D0 / ninterps
if (ninterps .eq. 0 .or. ninterps .gt. 3) then
print *,"NINTERPS error", ninterps
STOP
endif
sfrac = (xfrac + yfrac + zfrac) * oonints
onemsfrac = 1.0D0 - sfrac
c Once again some c-preprocessor tricks based on the whole fortran
c space thing...
#define INTPOINT(f,v) f(i,j,k) = sfrac * v + onemsfrac * f(i,j,k)
#define intone(f) INTPOINT(f, f e)
#define int_grp(p) \
intone(p xx) &&\
intone(p xy) &&\
intone(p xz) &&\
intone(p yy) &&\
intone(p yz) &&\
intone(p zz)
if (doGij) then
int_grp(g)
endif
if (doKij) then
int_grp(k)
endif
if (doLapse) then
intone(alp)
endif
if (doShift.and.(shift_state.ne.0)) then
intone(betax)
intone(betay)
intone(betaz)
endif
endif ! r > rinner
enddo
enddo
enddo
return
end
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