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c -*-Fortran-*-
c $Header:$
#include "cctk.h"
c$$$ This routine performs "TVD" prolongation. It is intended to be used
c$$$ with GFs that are not expected to be smooth, particularly those
c$$$ that must also obey certain constraints. The obvious example is the
c$$$ density in hydrodynamics, which may be discontinuous yet must be
c$$$ strictly positive.
c$$$
c$$$ To ensure that this prolongation method is used you should add the
c$$$ tag
c$$$
c$$$ tags='Prolongation="TVD"'
c$$$
c$$$ to the interface.ccl on the appropriate group.
c$$$
c$$$ This applies minmod type limiting to the slope, checking over the
c$$$ entire coarse grid cell for the minimum modulus in each direction.
c$$$
c$$$ The actual minmod function is defined in the routine
c$$$
c$$$ prolongate_3d_real8_minmod.F77
#define CHKIDX(i,j,k, imax,jmax,kmax, where) \
if ((i).lt.1 .or. (i).gt.(imax) \
.or. (j).lt.1 .or. (j).gt.(jmax) \
.or. (k).lt.1 .or. (k).gt.(kmax)) then &&\
write (msg, '(a, " array index out of bounds: shape is (",i4,",",i4,",",i4,"), index is (",i4,",",i4,",",i4,")")') \
(where), (imax), (jmax), (kmax), (i), (j), (k) &&\
call CCTK_WARN (0, msg(1:len_trim(msg))) &&\
end if
function minmod(a, b)
implicit none
CCTK_REAL8 minmod
CCTK_REAL8 a, b
CCTK_REAL8 zero
parameter (zero = 0)
if (a * b .lt. zero) then
minmod = zero
else if (abs(a) < abs(b)) then
minmod = a
else
minmod = b
end if
end function
subroutine prolongate_3d_real8_minmod (
$ src, srciext, srcjext, srckext,
$ dst, dstiext, dstjext, dstkext,
$ srcbbox, dstbbox, regbbox)
implicit none
CCTK_REAL8 one
parameter (one = 1)
integer srciext, srcjext, srckext
CCTK_REAL8 src(srciext,srcjext,srckext)
integer dstiext, dstjext, dstkext
CCTK_REAL8 dst(dstiext,dstjext,dstkext)
c bbox(:,1) is lower boundary (inclusive)
c bbox(:,2) is upper boundary (inclusive)
c bbox(:,3) is stride
integer srcbbox(3,3), dstbbox(3,3), regbbox(3,3)
integer offsetlo, offsethi
integer regiext, regjext, regkext
integer dstifac, dstjfac, dstkfac
integer srcioff, srcjoff, srckoff
integer dstioff, dstjoff, dstkoff
integer i, j, k
integer i0, j0, k0
integer fi, fj, fk
integer ifac(4), jfac(4), kfac(4)
integer ii, jj, kk
integer fac
CCTK_REAL8 res
integer d
character msg*1000
external minmod
CCTK_REAL8 minmod
CCTK_REAL8 half, zero
parameter (half = 0.5)
parameter (zero = 0)
CCTK_REAL8 dupw, dloc, slopex, slopey, slopez
logical firstloop
do d=1,3
if (srcbbox(d,3).eq.0 .or. dstbbox(d,3).eq.0
$ .or. regbbox(d,3).eq.0) then
call CCTK_WARN (0, "Internal error: stride is zero")
end if
if (srcbbox(d,3).le.regbbox(d,3)
$ .or. dstbbox(d,3).ne.regbbox(d,3)) then
call CCTK_WARN (0, "Internal error: strides disagree")
end if
if (mod(srcbbox(d,3), dstbbox(d,3)).ne.0) then
call CCTK_WARN (0, "Internal error: destination strides are not integer multiples of the source strides")
end if
if (mod(srcbbox(d,1), srcbbox(d,3)).ne.0
$ .or. mod(dstbbox(d,1), dstbbox(d,3)).ne.0
$ .or. mod(regbbox(d,1), regbbox(d,3)).ne.0) then
call CCTK_WARN (0, "Internal error: array origins are not integer multiples of the strides")
end if
if (regbbox(d,1).gt.regbbox(d,2)) then
c This could be handled, but is likely to point to an error elsewhere
call CCTK_WARN (0, "Internal error: region extent is empty")
end if
if (mod(srcbbox(d,2) - srcbbox(d,1), srcbbox(d,3)).ne.0
$ .or. mod(dstbbox(d,2) - dstbbox(d,1), dstbbox(d,3)).ne.0
$ .or. mod(regbbox(d,2) - regbbox(d,1), regbbox(d,3)).ne.0) then
call CCTK_WARN (0, "Internal error: array extents are not integer multiples of the strides")
end if
regkext = (regbbox(d,2) - regbbox(d,1)) / regbbox(d,3) + 1
dstkfac = srcbbox(d,3) / dstbbox(d,3)
srckoff = (regbbox(d,1) - srcbbox(d,1)) / dstbbox(d,3)
offsetlo = regbbox(d,3)
if (mod(srckoff + 0, dstkfac).eq.0) then
offsetlo = 0
if (regkext.gt.1) then
offsetlo = regbbox(d,3)
end if
end if
offsethi = regbbox(d,3)
if (mod(srckoff + regkext-1, dstkfac).eq.0) then
offsethi = 0
if (regkext.gt.1) then
offsethi = regbbox(d,3)
end if
end if
if (regbbox(d,1)-offsetlo.lt.srcbbox(d,1)
$ .or. regbbox(d,2)+offsethi.gt.srcbbox(d,2)
$ .or. regbbox(d,1).lt.dstbbox(d,1)
$ .or. regbbox(d,2).gt.dstbbox(d,2)) then
call CCTK_WARN (0, "Internal error: region extent is not contained in array extent")
end if
end do
if (srciext.ne.(srcbbox(1,2)-srcbbox(1,1))/srcbbox(1,3)+1
$ .or. srcjext.ne.(srcbbox(2,2)-srcbbox(2,1))/srcbbox(2,3)+1
$ .or. srckext.ne.(srcbbox(3,2)-srcbbox(3,1))/srcbbox(3,3)+1
$ .or. dstiext.ne.(dstbbox(1,2)-dstbbox(1,1))/dstbbox(1,3)+1
$ .or. dstjext.ne.(dstbbox(2,2)-dstbbox(2,1))/dstbbox(2,3)+1
$ .or. dstkext.ne.(dstbbox(3,2)-dstbbox(3,1))/dstbbox(3,3)+1) then
call CCTK_WARN (0, "Internal error: array sizes don't agree with bounding boxes")
end if
regiext = (regbbox(1,2) - regbbox(1,1)) / regbbox(1,3) + 1
regjext = (regbbox(2,2) - regbbox(2,1)) / regbbox(2,3) + 1
regkext = (regbbox(3,2) - regbbox(3,1)) / regbbox(3,3) + 1
dstifac = srcbbox(1,3) / dstbbox(1,3)
dstjfac = srcbbox(2,3) / dstbbox(2,3)
dstkfac = srcbbox(3,3) / dstbbox(3,3)
srcioff = (regbbox(1,1) - srcbbox(1,1)) / dstbbox(1,3)
srcjoff = (regbbox(2,1) - srcbbox(2,1)) / dstbbox(2,3)
srckoff = (regbbox(3,1) - srcbbox(3,1)) / dstbbox(3,3)
dstioff = (regbbox(1,1) - dstbbox(1,1)) / dstbbox(1,3)
dstjoff = (regbbox(2,1) - dstbbox(2,1)) / dstbbox(2,3)
dstkoff = (regbbox(3,1) - dstbbox(3,1)) / dstbbox(3,3)
c Loop over fine region
do k = 0, regkext-1
k0 = (srckoff + k) / dstkfac
fk = mod(srckoff + k, dstkfac)
do j = 0, regjext-1
j0 = (srcjoff + j) / dstjfac
fj = mod(srcjoff + j, dstjfac)
do i = 0, regiext-1
i0 = (srcioff + i) / dstifac
fi = mod(srcioff + i, dstifac)
slopex = zero
slopey = zero
slopez = zero
firstloop = .true.
do kk = 1, 2
do jj = 1, 2
dupw = src(i0+1 ,j0+jj,k0+kk) - src(i0+0 ,j0+jj,k0+kk)
dloc = src(i0+2 ,j0+jj,k0+kk) - src(i0+1 ,j0+kk,k0+kk)
if (firstloop) then
slopex = half * dble(fi) * minmod(dupw,dloc)
firstloop = .false.
else
slopex =
$ minmod(slopex, half * dble(fi) * minmod(dupw,dloc))
end if
end do
end do
firstloop = .true.
do kk = 1, 2
do ii = 1, 2
dupw = src(i0+ii,j0+1 ,k0+kk) - src(i0+ii,j0+0 ,k0+kk)
dloc = src(i0+ii,j0+2 ,k0+kk) - src(i0+ii,j0+1 ,k0+kk)
if (firstloop) then
slopey = half * dble(fj) * minmod(dupw,dloc)
firstloop = .false.
else
slopey =
$ minmod(slopey, half * dble(fj) * minmod(dupw,dloc))
end if
end do
end do
firstloop = .true.
do jj = 1, 2
do ii = 1, 2
dupw = src(i0+ii,j0+jj,k0+1 ) - src(i0+ii,j0+jj,k0+0 )
dloc = src(i0+ii,j0+jj,k0+2 ) - src(i0+ii,j0+jj,k0+1 )
if (firstloop) then
slopez = half * dble(fk) * minmod(dupw,dloc)
firstloop = .false.
else
slopez =
$ minmod(slopez, half * dble(fk) * minmod(dupw,dloc))
end if
end do
end do
CHKIDX (dstioff+i+1, dstjoff+j+1, dstkoff+k+1, \
dstiext,dstjext,dstkext, "destination")
dst (dstioff+i+1, dstjoff+j+1, dstkoff+k+1) =
. src(i0+1,j0+1,k0+1) + slopex + slopey + slopez
end do
end do
end do
end
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