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Copy pathmod_tsadvc.F
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mod_tsadvc.F
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#if defined(ROW_LAND)
#define SEA_P .true.
#define SEA_U .true.
#define SEA_V .true.
#elif defined(ROW_ALLSEA)
#define SEA_P allip(j).or.ip(i,j).ne.0
#define SEA_U alliu(j).or.iu(i,j).ne.0
#define SEA_V alliv(j).or.iv(i,j).ne.0
#else
#define SEA_P ip(i,j).ne.0
#define SEA_U iu(i,j).ne.0
#define SEA_V iv(i,j).ne.0
#endif
module mod_tsadvc
use mod_xc ! HYCOM communication interface
use mod_pipe ! HYCOM debugging interface
use mod_nc ! HYCOM netcdf output (debug)
implicit none
c
c --- module for tsadvc and related routines
c
private !! default is private
public :: tsadvc
c
integer, parameter, dimension (0:4) ::
& mbdy_advtyp = (/ 2, !PCM
& 5, !MPDATA
& 5, !FCT2
& 5, !FCT2C
& 5 /) !FCT4
c
logical, parameter :: lpipe_advem=.false. !extra checking (when pipe on)
logical, parameter :: lconserve =.false. !explicitly conserve the field
c
#if defined(RELO)
real, save, allocatable, dimension(:,:) ::
#else
real, save, dimension(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) ::
#endif
& fmx,fmn ! local max,min
& ,flx,fly ! fluxes
& ,fldlo ! lo order solution
& ,fmxlo,fmnlo ! local min
& ,fax,fay ! fluxes
& ,rp,rm ! FCT/MPDATA terms
& ,flxdiv ! flux divergence
& ,tx1,ty1 ! MPDATA terms
& ,fldao,fldan ! total field quantity (old/center, new)
#if defined(RELO)
real, save, allocatable, dimension(:,:) ::
#else
real, save, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy)::
#endif
& uloc,vloc,hloc,dtloc,ucumdt,vcumdt,flxcum,flycum
#if defined(RELO)
logical, save, allocatable, dimension(:,:) ::
#else
logical, save, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy)::
#endif
& lcalc
contains
! subroutine advem(advtyp,fld,fldc,u,v,fco,fcn,posdef,
! & scal,scali,dt2)
subroutine advem(advtyp,fld,fldc,u,v,fco,fcn,posdef, !!Alex river
& scal,scali,dt2,aux1)
implicit none
c
integer, intent(in) :: advtyp
real, intent(in) :: posdef,dt2
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& intent(inout) :: fld
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& intent(in) :: fldc,u,v,fco,fcn,scal,scali
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& intent(in),optional :: aux1
c
c --- wrapper for advection schemes
c
c --- a recent text on advection schemes is:
c --- D.R. Durran (1999): Numerical Methods for wave equations in
c --- geophysical fluid dynamics, Springer.
c
c --- advtyp= 0 for 1st order PCM (Donor Cell)
c --- advtyp= 1 for 2nd order MPDATA (old to new, as in 2.1.03)
c --- advtyp= 2 for 2nd order FCT (Leapfrog time step)
c --- advtyp= 4 for 4th order FCT (Leapfrog time step)
c
c --- time steps are "old", "center" and "new".
c
c --- fld - scalar field, at old time step on input but new on output
c --- fldc - scalar field, at center time step
c --- u,v - mass fluxes satisfying continuity equation (old to new)
c --- fco - thickness of the layer at old time step
c --- fcn - thickness of the layer at new time step
c --- posdef - offset for MPDATA to make the field positive
c --- scal - spatial increments (squared)
c --- scali - inverse of scal
c --- dt2 - temporal increment (from old to new, i.e. two time steps)
c
c on return, fld's valid halo will be 0 wide.
c
real offset
real*8 sumold,sumnew,sumcor
integer i,j
c
#if defined(RELO)
if (.not.allocated(fmx)) then
allocate(
& fmx(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& fmn(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& flx(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& fly(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& fldlo(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& fmxlo(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& fmnlo(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& fax(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& fay(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& rp(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& rm(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& flxdiv(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& tx1(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& ty1(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& fldao(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& fldan(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) )
call mem_stat_add( 16*(idm+2*nbdy)*(jdm+2*nbdy) )
fmx = r_init
fmn = r_init
flx = r_init
fly = r_init
fldlo = r_init
fmxlo = r_init
fmnlo = r_init
fax = r_init
fay = r_init
rp = r_init
rm = r_init
flxdiv = r_init
tx1 = r_init
ty1 = r_init
fldao = r_init
fldan = r_init
allocate(
& uloc(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& vloc(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& hloc(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& dtloc(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& ucumdt(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& vcumdt(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& flxcum(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& flycum(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& lcalc(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy))
call mem_stat_add( 9*(idm+2*nbdy)*(jdm+2*nbdy) )
uloc = r_init
vloc = r_init
hloc = r_init
dtloc = r_init
ucumdt = r_init
vcumdt = r_init
flxcum = r_init
flycum = r_init
lcalc = .false.
endif !.not.allocated
#endif
c
if (advtyp.eq.0) then
call advem_pcm( fld, u,v,fco,fcn, scal,scali,dt2)
elseif (advtyp.eq.1) then
call advem_mpdata(fld, u,v,fco,fcn,posdef,scal,scali,dt2)
elseif (advtyp.eq.2) then
call advem_fct2( fld,fldc,u,v,fco,fcn, scal,scali,dt2)
elseif (advtyp.eq.3) then !btrmas
! call advem_fct2c( fld,fldc,u,v,fco,fcn, scal,scali,dt2)
if (rivrtr.eq.1) then
call advem_fct2c( fld,fldc,u,v,fco,fcn,scal,scali,dt2,aux1) !!Alex river
else
call advem_fct2c( fld,fldc,u,v,fco,fcn, scal,scali,dt2)
endif
elseif (advtyp.eq.4) then
call advem_fct4( fld,fldc,u,v,fco,fcn, scal,scali,dt2)
else
if (mnproc.eq.1) then
write(lp,'(/ a,i4 /)')
& 'error: advem called with advtyp =',advtyp
endif
call xcstop('advem')
stop 'advem'
endif
c
if (lconserve) then !usually .false.
c
c --- explicit conservation of tracer (should not be needed).
c
call xcsum(sumold, fldao,ipa)
call xcsum(sumnew, fldan,ipa)
c
if (sumnew.ne.0.0) then
offset = (sumold-sumnew)/sumnew
else
offset = 0.0
endif
c
!$OMP PARALLEL DO PRIVATE(j,i,offset)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1,jj
do i=1,ii
if (SEA_P) then
fld(i,j)=fld(i,j)*(1.0+offset)
c
cdiag fldan(i,j) = fld(i,j)*fcn(i,j)*scal(i,j)
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
call pipe_compare_sym1(fld, ip,'ad:oset:fld ')
endif
c
cdiag call xcsum(sumcor, fldan,ipa)
cdiag if (mnproc.eq.1) then
cdiag write(lp,'(a,1p4e16.8)')
cdiag& 'advem: ',sumold,sumnew,sumcor,offset
cdiag endif
endif !lconserve
return
end subroutine advem
subroutine advem_mpdata(fld,u,v,fco,fcn,posdef,scal,scali,dt2)
implicit none
c
real, intent(in) :: posdef,dt2
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& intent(inout) :: fld
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& intent(in) :: u,v,scal,scali,fco,fcn
c
c LeapFrog 2nd order MPDATA.
c combined monotone scheme, for details see section 3.3 (eqs. 34 to 37)
c in smolarkiewicz and clark, 1986, j.comput.phys.,67,no 2, p. 396-438
c and smolarkiewicz and grabowski, 1989, j.comput.phys. and recently
c P.K. Smolarkiewicz and L.J. Margolin (1998): MPDATA: A finite
c difference solver for geophysical flows, J.Comput.Phys. 140 459-480.
c
c time steps are "old", "center" and "new".
c
c fld - scalar field, must be >0, old input but new output
c u,v - mass fluxes satisfying continuity equation (old to new)
c fco - thickness of the layer at old time step
c fcn - thickness of the layer at new time step
c posdef - offset to make the field positive
c scal - spatial increments (squared)
c scali - inverse of scal
c dt2 - temporal increment (from old to new)
c
c on return, fld's valid halo will be 0 wide.
c
real, parameter :: onemu=9806.e-12 !very small layer thickness
c
real fcn2,fco2,flxdn,flxdp,flydn,flydp,q
integer i,j,l,ia,ib,ja,jb,mbdy_a,margin
c
integer itest,jtest,ittest,jttest
common/testpt/itest,jtest,ittest,jttest
save /testpt/
c
mbdy_a = mbdy_advtyp(1) ! = 5
c
c --- compute low-order and part of antidiffusive fluxes
c
c --- rhs: u, v, fld+
c --- lhs: flx, fly, fmx, fmn
c
margin = mbdy_a - 1
c
!$OMP PARALLEL DO PRIVATE(j,i,q,jb,ja,ib,ia)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_U) then
tx1(i,j)=.5*abs(u(i,j))*(fld(i,j)-fld(i-1,j))
if (u(i,j).ge.0.0) then
q=fld(i-1,j)
else
q=fld(i ,j)
endif
flx(i,j)=u(i,j)*(q+posdef)
endif !iu
if (SEA_V) then
ty1(i,j)=.5*abs(v(i,j))*(fld(i,j)-fld(i,j-1))
if (v(i,j).ge.0.0) then
q=fld(i,j-1)
else
q=fld(i,j )
endif
fly(i,j)=v(i,j)*(q+posdef)
endif !iv
if (SEA_P) then
ia=ipim1(i,j) !i-1 if sea and i if land
ib=ipip1(i,j) !i+1 if sea and i if land
ja=ipjm1(i,j) !j-1 if sea and j if land
jb=ipjp1(i,j) !j+1 if sea and j if land
fmx(i,j)=max(fld(i,j),fld(ia,j),fld(ib,j),
& fld(i,ja),fld(i,jb))+posdef
fmn(i,j)=min(fld(i,j),fld(ia,j),fld(ib,j),
& fld(i,ja),fld(i,jb))+posdef
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
c
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
call pipe_compare_sym2(tx1, iu,'ad:11:tx1 ',
& ty1, iv,'ad:11:ty1 ')
call pipe_compare_sym2(flx, iu,'ad:11:flx ',
& fly, iv,'ad:11:fly ')
call pipe_compare_sym1(fmx, ip,'ad:11:fmx ')
call pipe_compare_sym1(fmn, ip,'ad:11:fmn ')
endif
c
c --- rhs: u, v, fld+
c --- lhs: flx, fly, fmx, fmn
c
margin = mbdy_a - 1
c
do j=1-margin,jj+margin
do l=1,isp(j) !ok
if (ifp(j,l).ge. 1-margin) then
flx(ifp(j,l) ,j)=0.0
endif
if (ilp(j,l).lt.ii+margin) then
flx(ilp(j,l)+1,j)=0.0
endif
enddo !l
enddo !j
c
do i=1-margin,ii+margin
do l=1,jsp(i) !ok
if (jfp(i,l).ge. 1-margin) then
fly(i,jfp(i,l) )=0.0
endif
if (jlp(i,l).lt.jj+margin) then
fly(i,jlp(i,l)+1)=0.0
endif
enddo !l
enddo !i
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
call pipe_compare_sym2(flx, iu,'ad:22:flx ',
& fly, iv,'ad:33:fly ')
endif
cdiag if (itest.gt.0 .and. jtest.gt.0) then
cdiag i=itest
cdiag j=jtest
cdiag write (lp,'(a,2i5,f22.3/1pe39.2/0pf21.3,1pe9.2,0pf9.3,
cdiag. 1pe9.2,0pf9.3/1pe39.2/0pf39.3)')
cdiag. 'advem (1)',i+i0,j+j0,
cdiag. fld(i-1,j),u(i,j),fld(i,j-1),v(i,j),
cdiag. fld(i,j),v(i,j+1),fld(i,j+1),u(i+1,j),fld(i+1,j)
cdiag endif
c
c --- rhs: flx+, fly+, fco, fmn, fmx, fcn
c --- lhs: fld
c
margin = mbdy_a - 2
c
!$OMP PARALLEL DO PRIVATE(j,i,q)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
!...........lo order Donor Cell step
flxdiv(i,j)=((flx(i+1,j)-flx(i,j))+
& (fly(i,j+1)-fly(i,j)) )*dt2*scali(i,j)
q=(fld(i,j)+posdef)*(fco(i,j)+onemu)-flxdiv(i,j)
!max,min should only be active for very thin layers
fldlo(i,j)=max( fmn(i,j), min( fmx(i,j),
& q/(fcn(i,j)+onemu) ))
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
call pipe_compare_sym1(fldlo, ip,'ad:610:fldlo')
call pipe_compare_sym1(flxdiv, ip,'ad:610:flxdv')
endif
c
c --- finish computation of antidiffusive fluxes
c
c --- rhs: tx1, u, ty1, v, flxdiv+, fco+, fcn+
c --- lhs: flx, fly
c
margin = mbdy_a - 2
c
!$OMP PARALLEL DO PRIVATE(j,i,fcn2,fco2)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
fco2=0.0
fcn2=0.0
do i=1-margin,ii+margin
if (SEA_U) then
fco2=fco(i,j)+fco(i-1,j) ! inforce order on flx calc
fcn2=fcn(i,j)+fcn(i-1,j) ! inforce order on flx calc
flx(i,j)=tx1(i,j)-u(i,j)*(flxdiv(i,j)+flxdiv(i-1,j))
& /((fco2+fcn2)+onemu)
endif !iu
if (SEA_V) then
fco2=fco(i,j)+fco(i,j-1) ! inforce order on fly calc
fcn2=fcn(i,j)+fcn(i,j-1) ! inforce order on fly calc
fly(i,j)=ty1(i,j)-v(i,j)*(flxdiv(i,j)+flxdiv(i,j-1))
& /((fco2+fcn2)+onemu)
endif !iv
enddo !i
if (fco2*fcn2.eq.1.e30) flx(1-nbdy,j)=0.0 ! prevent removal of fc*2
enddo !j
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
call pipe_compare_sym2(flx, iu,'ad: 8:flx ',
& fly, iv,'ad: 8:fly ')
endif
c
c --- limit antidiffusive fluxes
c --- rp and rm used to be called flp and fln
c
c --- rhs: fmx, fmn, fldlo, fcn, flx+, fly+
c --- lhs: rp, rm
c
margin = mbdy_a - 3
c
!$OMP PARALLEL DO PRIVATE(j,i,flxdn,flxdp,flydn,flydp)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
flxdp=min(0.0,flx(i+1,j))-max(0.0,flx(i,j))
flxdn=max(0.0,flx(i+1,j))-min(0.0,flx(i,j))
flydp=min(0.0,fly(i,j+1))-max(0.0,fly(i,j))
flydn=max(0.0,fly(i,j+1))-min(0.0,fly(i,j))
rp(i,j)=(fmx(i,j)-fldlo(i,j))*(fcn(i,j)*scal(i,j))/
& ((onemu-(flxdp+flydp))*dt2)
rm(i,j)=(fldlo(i,j)-fmn(i,j))*(fcn(i,j)*scal(i,j))/
& ((onemu+(flxdn+flydn))*dt2)
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
call pipe_compare_sym1(rp, ip,'ad:16:flp ')
call pipe_compare_sym1(rm, ip,'ad:16:fln ')
endif
c
c --- rhs: flx, fly, rp+, rm+
c --- lhs: flx, fly
c
margin = mbdy_a - 4
c
!$OMP PARALLEL DO PRIVATE(j,i)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_U) then
flx(i,j)=max(0.0,flx(i,j))*min(1.0,rp(i,j),rm(i-1,j))
& +min(0.0,flx(i,j))*min(1.0,rp(i-1,j),rm(i,j))
endif !iu
if (SEA_V) then
fly(i,j)=max(0.0,fly(i,j))*min(1.0,rp(i,j),rm(i,j-1))
& +min(0.0,fly(i,j))*min(1.0,rp(i,j-1),rm(i,j))
endif !iv
enddo !i
enddo !j
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
call pipe_compare_sym2(flx, iu,'ad:18:flx ',
& fly, iv,'ad:18:fly ')
endif
c
cdiag i=itest
cdiag j=jtest
cdiag write (lp,'(''advem (2)'',2i5,f22.3/1pe39.2/0pf21.3,1pe9.2,0pf9.3,
cdiag.1pe9.2,0pf9.3/1pe39.2/0pf39.3)') i,j,fldlo(i-1,j),u(i,j),fldlo(i,j-1),
cdiag.v(i,j),fldlo(i,j),v(i,j+1),fldlo(i,j+1),u(i+1,j),fldlo(i+1,j)
c
c --- rhs: flx+, fly+, fldlo, fcn, fmx
c --- lhs: flxdiv, fld
c
margin = mbdy_a - 5
c
!$OMP PARALLEL DO PRIVATE(j,i)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
fldao(i,j) = fld(i,j)*fco(i,j)*scal(i,j)
c
!...........apply antidiffusive flux correction
flxdiv(i,j)=((flx(i+1,j)-flx(i,j))+
& (fly(i,j+1)-fly(i,j)) )*dt2*scali(i,j)
!max,min should only be active for very thin layers
fld(i,j)=max( fmn(i,j), min( fmx(i,j),
& fldlo(i,j)-flxdiv(i,j)/(fcn(i,j)+onemu) ))
fld(i,j)=fld(i,j)-posdef
c
fldan(i,j) = fld(i,j)*fcn(i,j)*scal(i,j)
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
call pipe_compare_sym1(flxdiv, ip,'ad:620:flxdv')
call pipe_compare_sym1(fld, ip,'ad:1620:fld ')
endif
return
end subroutine advem_mpdata
subroutine advem_pcm(fld,u,v,fco,fcn,scal,scali,dt2)
implicit none
c
real, intent(in) :: dt2
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& intent(inout) :: fld
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& intent(in) :: u,v,scal,scali,fco,fcn
c
c Piecewise Constant Method (Donor Cell, Upwind)
c Over two time steps (may require half the normal time step for stability).
c
c time steps are "old", "center" and "new".
c
c fld - scalar field, need not be >0, old input but new output
c u,v - mass fluxes satisfying continuity equation (old to new)
c fco - thickness of the layer at old time step
c fcn - thickness of the layer at new time step
c scal - spatial increments (squared)
c scali - inverse of scal
c dt2 - temporal increment (from old to new)
c
c on return, fld's valid halo will be 0 wide.
c
real, parameter :: onemu=9806.e-12 !very small layer thickness
real, parameter :: onecm=98.06 !one cm in pressure units
c
real q
integer i,j,l,ia,ib,ja,jb,mbdy_a,margin
c
integer itest,jtest,ittest,jttest
common/testpt/itest,jtest,ittest,jttest
save /testpt/
c
c --- rhs: u, v, fld+
c --- lhs: flx, fly
c
mbdy_a = mbdy_advtyp(0) ! = 2
c
margin = mbdy_a - 1
c
!$OMP PARALLEL DO PRIVATE(j,i,q)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_U) then
if (u(i,j).ge.0.0) then
q=fld(i-1,j)
else
q=fld(i ,j)
endif
flx(i,j)=u(i,j)*q
endif !iu
if (SEA_V) then
if (v(i,j).ge.0.0) then
q=fld(i,j-1)
else
q=fld(i,j )
endif
fly(i,j)=v(i,j)*q
endif !iv
if (SEA_P) then
ia=ipim1(i,j) !i-1 if sea and i if land
ib=ipip1(i,j) !i+1 if sea and i if land
ja=ipjm1(i,j) !j-1 if sea and j if land
jb=ipjp1(i,j) !j+1 if sea and j if land
fmx(i,j)=max(fld(i,j),fld(ia,j),fld(ib,j),
& fld(i,ja),fld(i,jb))
fmn(i,j)=min(fld(i,j),fld(ia,j),fld(ib,j),
& fld(i,ja),fld(i,jb))
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
c
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
call pipe_compare_sym2(flx, iu,'ad:11:flx ',
& fly, iv,'ad:11:fly ')
endif
c
do j=1-margin,jj+margin
do l=1,isp(j) !ok
if (ifp(j,l).ge. 1-margin) then
flx(ifp(j,l) ,j)=0.0
endif
if (ilp(j,l).lt.ii+margin) then
flx(ilp(j,l)+1,j)=0.0
endif
enddo !l
enddo !j
c
do i=1-margin,ii+margin
do l=1,jsp(i) !ok
if (jfp(i,l).ge. 1-margin) then
fly(i,jfp(i,l) )=0.0
endif
if (jlp(i,l).lt.jj+margin) then
fly(i,jlp(i,l)+1)=0.0
endif
enddo !l
enddo !i
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
call pipe_compare_sym2(flx, iu,'ad:22:flx ',
& fly, iv,'ad:33:fly ')
endif
cdiag if (itest.gt.0 .and. jtest.gt.0) then
cdiag i=itest
cdiag j=jtest
cdiag write (lp,'(a,2i5,f22.3/1pe39.2/0pf21.3,1pe9.2,0pf9.3,
cdiag. 1pe9.2,0pf9.3/1pe39.2/0pf39.3)')
cdiag. 'advem (1)',i+i0,j+j0,
cdiag. fld(i-1,j),u(i,j),fld(i,j-1),v(i,j),
cdiag. fld(i,j),v(i,j+1),fld(i,j+1),u(i+1,j),fld(i+1,j)
cdiag endif
c
c --- rhs: flx+, fly+, fld, fco, fcn
c --- lhs: flxdiv, fld
c
margin = mbdy_a - 2
c
!$OMP PARALLEL DO PRIVATE(j,i,q)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
fldao(i,j) = fld(i,j)*fco(i,j)*scal(i,j)
c
flxdiv(i,j)=((flx(i+1,j)-flx(i,j))+
& (fly(i,j+1)-fly(i,j)) )*dt2*scali(i,j)
q=fld(i,j)*(fco(i,j)+onemu)-flxdiv(i,j)
!max,min should only be active for very thin layers
fld(i,j)=max( fmn(i,j), min( fmx(i,j),
& q/(fcn(i,j)+onemu) ))
c
fldan(i,j) = fld( i,j)*fcn(i,j)*scal(i,j)
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
call pipe_compare_sym1(fld, ip,'ad:610:fld ')
call pipe_compare_sym1(flxdiv, ip,'ad:610:flxdv')
endif
c
cdiag i=itest
cdiag j=jtest
cdiag write (lp,'(''advem (2)'',2i5,f22.3/1pe39.2/0pf21.3,1pe9.2,0pf9.3,
cdiag.1pe9.2,0pf9.3/1pe39.2/0pf39.3)') i,j,fld(i-1,j),u(i,j),fld(i,j-1),
cdiag.v(i,j),fld(i,j),v(i,j+1),fld(i,j+1),u(i+1,j),fld(i+1,j)
return
end subroutine advem_pcm
subroutine advem_fct2(fld,fldc,u,v,fco,fcn,scal,scali,dt2)
implicit none
c
real, intent(in) :: dt2
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& intent(inout) :: fld
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy),
& intent(in) :: fldc,u,v,scal,scali,fco,fcn
c
c Leapfrog 2nd order FCT
c S.T. Zalesak (1979): Fully multidimensional flux-corrected
c transport algorithms for fluids, J.Comput.Phys. 31 335-362.
c
c time steps are "old", "center" and "new".
c
c fld - scalar field, need not be >0, old input but new output
c fldc - scalar field at center time step
c u,v - mass fluxes satisfying continuity equation (old to new)
c fco - thickness of the layer at old time step
c fcn - thickness of the layer at new time step
c scal - spatial increments (squared)
c scali - inverse of scal
c dt2 - temporal increment (from old to new)
c
c on return, fld's valid halo will be 0 wide.
c
real, parameter :: onemu=9806.e-12 !very small layer thickness
real, parameter :: epsil=1.e-20
c
real flxdn,flxdp,flydn,flydp,q
integer i,j,l,ia,ib,ja,jb,mbdy_a,margin
c
integer itest,jtest,ittest,jttest
common/testpt/itest,jtest,ittest,jttest
save /testpt/
c
real :: fhx, fhy, fqmax, fqmin, famax, famin
real :: qdt2, qp, qm, fact
mbdy_a = mbdy_advtyp(2) ! = 5
c
c --- compute low-order and part of antidiffusive fluxes
c
c --- rhs: u, v, fld+
c --- lhs: flx, fly, fmx, fmn
c
margin = mbdy_a - 1
c
!$OMP PARALLEL DO PRIVATE(j,i,q,jb,ja,ib,ia)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_U) then
if (u(i,j).ge.0.0) then
q=fld(i-1,j)
else
q=fld(i ,j)
endif
flx(i,j)=u(i,j)*q
endif !iu
if (SEA_V) then
if (v(i,j).ge.0.0) then
q=fld(i,j-1)
else
q=fld(i,j )
endif
fly(i,j)=v(i,j)*q
endif !iv
if (SEA_P) then
ia=ipim1(i,j) !i-1 if sea and i if land
ib=ipip1(i,j) !i+1 if sea and i if land
ja=ipjm1(i,j) !j-1 if sea and j if land
jb=ipjp1(i,j) !j+1 if sea and j if land
fmx(i,j)=max(fld(i,j),fld(ia,j),fld(ib,j),
& fld(i,ja),fld(i,jb))
fmn(i,j)=min(fld(i,j),fld(ia,j),fld(ib,j),
& fld(i,ja),fld(i,jb))
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
c
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
! call pipe_compare_sym2(tx1, iu,'ad:11:tx1 ',
! & ty1, iv,'ad:11:ty1 ')
! call pipe_compare_sym2(flx, iu,'ad:11:flx ',
! & fly, iv,'ad:11:fly ')
endif
c
do j=1-margin,jj+margin
do l=1,isp(j) !ok
if (ifp(j,l).ge. 1-margin) then
flx(ifp(j,l) ,j)=0.0
endif
if (ilp(j,l).lt.ii+margin) then
flx(ilp(j,l)+1,j)=0.0
endif
enddo !l
enddo !j
c
do i=1-margin,ii+margin
do l=1,jsp(i) !ok
if (jfp(i,l).ge. 1-margin) then
fly(i,jfp(i,l) )=0.0
endif
if (jlp(i,l).lt.jj+margin) then
fly(i,jlp(i,l)+1)=0.0
endif
enddo !l
enddo !i
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
call pipe_compare_sym2(flx, iu,'ad:22:flx ',
& fly, iv,'ad:33:fly ')
endif
cdiag if (itest.gt.0 .and. jtest.gt.0) then
cdiag i=itest
cdiag j=jtest
cdiag write (lp,'(a,2i5,f22.3/1pe39.2/0pf21.3,1pe9.2,0pf9.3,
cdiag. 1pe9.2,0pf9.3/1pe39.2/0pf39.3)')
cdiag. 'advem (1)',i+i0,j+j0,
cdiag. fld(i-1,j),u(i,j),fld(i,j-1),v(i,j),
cdiag. fld(i,j),v(i,j+1),fld(i,j+1),u(i+1,j),fld(i+1,j)
cdiag endif
c
c --- rhs: flx+, fly+, fld, fmx, fmn, fco, fcn
c --- lhs: fldlo, fmxlo, fmnlo, flxdiv
c
margin = mbdy_a - 2
c
!$OMP PARALLEL DO PRIVATE(j,i,q)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
!...........lo order Donor Cell step
flxdiv(i,j)=((flx(i+1,j)-flx(i,j))+
& (fly(i,j+1)-fly(i,j)) )*dt2*scali(i,j)
q=fld(i,j)*(fco(i,j)+onemu)-flxdiv(i,j)
!max,min should only be active for very thin layers
fldlo(i,j)=max( fmn(i,j), min( fmx(i,j),
& q/(fcn(i,j)+onemu) ))
fmxlo(i,j) = max(fld(i,j),fldc(i,j),fldlo(i,j))
fmnlo(i,j) = min(fld(i,j),fldc(i,j),fldlo(i,j))
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
call pipe_compare_sym1(fldlo, ip,'ad:610:fldlo')
call pipe_compare_sym1(flxdiv, ip,'ad:610:flxdv')
endif
c
!.....Leapfrog step using high order scheme
c
c --- rhs: u, v, fld+, flx, fly
c --- lhs: fax, fay
c
margin = mbdy_a - 2
c
!$OMP PARALLEL DO PRIVATE(j,i,q,jb,ja,ib,ia,fhx,fhy)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_U) then
fhx=u(i,j)*0.5*(fldc(i,j)+fldc(i-1,j)) ! 2nd order in space
fax(i,j)= fhx-flx(i,j) ! anti-diffusion x-flux
endif !iu
if (SEA_V) then
fhy=v(i,j)*0.5*(fldc(i,j)+fldc(i,j-1)) ! 2nd order in space
fay(i,j)= fhy-fly(i,j) ! anti-diffusion y-flux
endif !iv
enddo !i
enddo !j
!$OMP END PARALLEL DO
do j=1-margin,jj+margin
do l=1,isp(j) !ok
if (ifp(j,l).ge. 1-margin) then
fax(ifp(j,l) ,j)=0.0
endif
if (ilp(j,l).lt.ii+margin) then
fax(ilp(j,l)+1,j)=0.0
endif
enddo !l
enddo !j
c
do i=1-margin,ii+margin
do l=1,jsp(i) !ok
if (jfp(i,l).ge. 1-margin) then
fay(i,jfp(i,l) )=0.0
endif
if (jlp(i,l).lt.jj+margin) then
fay(i,jlp(i,l)+1)=0.0
endif
enddo !l
enddo !i
!========================================================
c
c --- finish computation of antidiffusive fluxes
c
c --- rhs: fmnlo+,fmxlo+,fax+,fay+,fldlo,fcn,scal
c --- lhs: rp, rm
c
margin = mbdy_a - 3
c
qdt2 = 1.0/dt2
!$OMP PARALLEL DO PRIVATE(j,i,ia,ib,ja,jb,
!$OMP& fqmax,fqmin,famax,famin,qp,qm)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
ia=ipim1(i,j) !i-1 if sea and i if land
ib=ipip1(i,j) !i+1 if sea and i if land
ja=ipjm1(i,j) !j-1 if sea and j if land
jb=ipjp1(i,j) !j+1 if sea and j if land
fqmax = max(fmxlo(i,j),fmxlo(ia,j),fmxlo(ib,j),
& fmxlo(i,ja),fmxlo(i,jb))
fqmin = min(fmnlo(i,j),fmnlo(ia,j),fmnlo(ib,j),
& fmnlo(i,ja),fmnlo(i,jb))
famax = max(0.0,fax(i, j) ) - min(0.0,fax(ib,j) ) +
& max(0.0,fay(i, j) ) - min(0.0,fay(i, jb))
famin = max(0.0,fax(ib,j) ) - min(0.0,fax(i, j) ) +
& max(0.0,fay(i, jb)) - min(0.0,fay(i, j) )
if (famax > 0.0) then
qp = (fqmax-fldlo(i,j)) *fcn(i,j)*scal(i,j)*qdt2
rp(i,j) = min(1.0, qp/famax)
else
rp(i,j) = 0.0
endif
if (famin > 0.0) then
qm = (fldlo(i,j)-fqmin) *fcn(i,j)*scal(i,j)*qdt2
rm(i,j) = min(1.0, qm/famin)
else
rm(i,j) = 0.0
endif
fmx(i,j) = fqmax !less restrictive maximum
fmn(i,j) = fqmin !less restrictive minimum
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
c
c --- rhs: rp+, rm+
c --- lhs: fax, fay
c
margin = mbdy_a - 4
c
!$OMP PARALLEL DO PRIVATE(j,i,fact)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_U) then
if (fax(i,j) < 0.0) then
fact = min(rp(i-1,j),rm(i,j))
else
fact = min(rp(i,j),rm(i-1,j))
endif
fax(i,j) = fact*fax(i,j)
endif !iu
if (SEA_V) then
if (fay(i,j) < 0.0) then
fact = min(rp(i,j-1),rm(i,j))
else
fact = min(rp(i,j),rm(i,j-1))
endif
fay(i,j) = fact*fay(i,j)
endif !iv
enddo !i
enddo !j
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
call pipe_compare_sym2(flx, iu,'ad:18:flx ',
& fly, iv,'ad:18:fly ')
endif
c
cdiag i=itest
cdiag j=jtest
cdiag write (lp,'(''advem (2)'',2i5,f22.3/1pe39.2/0pf21.3,1pe9.2,0pf9.3,
cdiag.1pe9.2,0pf9.3/1pe39.2/0pf39.3)') i,j,fldlo(i-1,j),u(i,j),fldlo(i,j-1),
cdiag.v(i,j),fldlo(i,j),v(i,j+1),fldlo(i,j+1),u(i+1,j),fldlo(i+1,j)
c
c --- rhs: fax+, fay+, fld, fcn, fmx, fmn
c --- lhs: fld
c
margin = mbdy_a - 5
c
!$OMP PARALLEL DO PRIVATE(j,i)
!$OMP& SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
fldao(i,j) = fld(i,j)*fco(i,j)*scal(i,j)
c
!...........apply antidiffusive flux correction
flxdiv(i,j)=((fax(i+1,j)-fax(i,j))+
& (fay(i,j+1)-fay(i,j)) )*dt2*scali(i,j)
!max,min should only be active for very thin layers
fld(i,j)=max( fmn(i,j), min( fmx(i,j),
& fldlo(i,j)-flxdiv(i,j)/(fcn(i,j)+onemu) ))
c
fldan(i,j) = fld(i,j)*fcn(i,j)*scal(i,j)
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
c --- compare two model runs.
call pipe_compare_sym1(flxdiv, ip,'ad:620:flxdv')
call pipe_compare_sym1(fld, ip,'ad:1620:fld ')
endif
return
end subroutine advem_fct2