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mod_tsadvc.F90
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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
implicit none
!
! --- module for tsadvc and related routines
!
private !! default is private
public :: tsadvc
!
integer, parameter, dimension (0:4) :: &
mbdy_advtyp = (/ 2, & !PCM
5, & !MPDATA
5, & !FCT2
0, & !N/A
5 /) !FCT4
!
logical, parameter :: lpipe_advem=.false. !extra checking (when pipe on)
logical, parameter :: lconserve =.false. !explicitly conserve the field
!
logical, save :: ldebug_tsdif !switch to debug diffusion - usually .false.
logical, save :: ldebug_advem !switch to debug advection - usually .false.
integer, save :: itests,jtests !local copy of itest,jtest
!
#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,btrmas)
implicit none
!
logical, intent(in) :: btrmas
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
!
! --- wrapper for advection schemes
!
! --- a recent text on advection schemes is:
! --- D.R. Durran (1999): Numerical Methods for wave equations in
! --- geophysical fluid dynamics, Springer.
!
! --- advtyp= 0 for 1st order PCM (Donor Cell)
! --- advtyp= 1 for 2nd order MPDATA (old to new, as in 2.1.03)
! --- advtyp= 2 for 2nd order FCT (Leapfrog time step)
! --- advtyp= 4 for 4th order FCT (Leapfrog time step)
!
! --- time steps are "old", "center" and "new".
!
! --- fld - scalar field, at old time step on input but new on output
! --- fldc - scalar field, at center time step
! --- u,v - mass fluxes satisfying continuity equation (old to new)
! --- fco - thickness of the layer at old time step
! --- fcn - thickness of the layer at new time step
! --- posdef - offset for MPDATA to make the field positive
! --- scal - spatial increments (squared)
! --- scali - inverse of scal
! --- dt2 - temporal increment (from old to new, i.e. two time steps)
!
! on return, fld's valid halo will be 0 wide.
!
real offset
real*8 sumold,sumnew,sumcor
integer i,j
!
#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
endif !.not.allocated
#endif
!
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 .and. btrmas) then
call advem_fct2c( fld,fldc,u,v,fco,fcn, scal,scali,dt2)
elseif (advtyp.eq.2) then !.not.btrmas
call advem_fct2( fld,fldc,u,v,fco,fcn, scal,scali,dt2)
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
!
if (lconserve) then !usually .false.
!
! --- explicit conservation of tracer (should not be needed).
!
call xcsum(sumold, fldao,ipa)
call xcsum(sumnew, fldan,ipa)
!
if (sumnew.ne.0.0) then
offset = (sumold-sumnew)/sumnew
else
offset = 0.0
endif
!
!$OMP PARALLEL DO PRIVATE(j,i,offset) &
!$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)
!
!diag fldan(i,j) = fld(i,j)*fcn(i,j)*scal(i,j)
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
! --- compare two model runs.
call pipe_compare_sym1(fld, ip,'ad:oset:fld ')
endif
!
!diag call xcsum(sumcor, fldan,ipa)
!diag if (mnproc.eq.1) then
!diag write(lp,'(a,1p4e16.8)') &
!diag 'advem: ',sumold,sumnew,sumcor,offset
!diag endif
endif !lconserve
return
end subroutine advem
subroutine advem_mpdata(fld,u,v,fco,fcn,posdef,scal,scali,dt2)
implicit none
!
real, intent(in) :: posdef,dt2
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
intent(inout) :: fld
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
intent(in) :: u,v,scal,scali,fco,fcn
!
! LeapFrog 2nd order MPDATA.
! combined monotone scheme, for details see section 3.3 (eqs. 34 to 37)
! in smolarkiewicz and clark, 1986, j.comput.phys.,67,no 2, p. 396-438
! and smolarkiewicz and grabowski, 1989, j.comput.phys. and recently
! P.K. Smolarkiewicz and L.J. Margolin (1998): MPDATA: A finite
! difference solver for geophysical flows, J.Comput.Phys. 140 459-480.
!
! time steps are "old", "center" and "new".
!
! fld - scalar field, must be >0, old input but new output
! u,v - mass fluxes satisfying continuity equation (old to new)
! fco - thickness of the layer at old time step
! fcn - thickness of the layer at new time step
! posdef - offset to make the field positive
! scal - spatial increments (squared)
! scali - inverse of scal
! dt2 - temporal increment (from old to new)
!
! on return, fld's valid halo will be 0 wide.
!
real, parameter :: onemu=9806.e-12 !very small layer thickness
!
real fcn2,fco2,flxdn,flxdp,flydn,flydp,q
integer i,j,l,ia,ib,ja,jb,mbdy_a,margin
!
mbdy_a = mbdy_advtyp(1) ! = 5
!
! --- compute low-order and part of antidiffusive fluxes
!
! --- rhs: u, v, fld+
! --- lhs: flx, fly, fmx, fmn
!
margin = mbdy_a - 1
!
!$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
!
if (lpipe .and. lpipe_advem) then
! --- 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
!
! --- rhs: u, v, fld+
! --- lhs: flx, fly, fmx, fmn
!
margin = mbdy_a - 1
!
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
!
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
! --- compare two model runs.
call pipe_compare_sym2(flx, iu,'ad:22:flx ', &
fly, iv,'ad:33:fly ')
endif
!diag if (itests.gt.0 .and. jtests.gt.0) then
!diag i=itests
!diag j=jtests
!diag write (lp,'(a,2i6,f22.3/1pe39.2/0pf21.3,1pe9.2,0pf9.3, &
!diag 1pe9.2,0pf9.3/1pe39.2/0pf39.3)') &
!diag 'advem (1)',i+i0,j+j0, &
!diag fld(i-1,j),u(i,j),fld(i,j-1),v(i,j), &
!diag fld(i,j),v(i,j+1),fld(i,j+1),u(i+1,j),fld(i+1,j)
!diag endif
!
! --- rhs: flx+, fly+, fco, fmn, fmx, fcn
! --- lhs: fld
!
margin = mbdy_a - 2
!
!$OMP PARALLEL DO PRIVATE(j,i,q) &
!$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
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
! --- compare two model runs.
call pipe_compare_sym1(fldlo, ip,'ad:610:fldlo')
call pipe_compare_sym1(flxdiv, ip,'ad:610:flxdv')
endif
!
! --- finish computation of antidiffusive fluxes
!
! --- rhs: tx1, u, ty1, v, flxdiv+, fco+, fcn+
! --- lhs: flx, fly
!
margin = mbdy_a - 2
!
!$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
! --- compare two model runs.
call pipe_compare_sym2(flx, iu,'ad: 8:flx ', &
fly, iv,'ad: 8:fly ')
endif
!
! --- limit antidiffusive fluxes
! --- rp and rm used to be called flp and fln
!
! --- rhs: fmx, fmn, fldlo, fcn, flx+, fly+
! --- lhs: rp, rm
!
margin = mbdy_a - 3
!
!$OMP PARALLEL DO PRIVATE(j,i,flxdn,flxdp,flydn,flydp) &
!$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
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
! --- compare two model runs.
call pipe_compare_sym1(rp, ip,'ad:16:flp ')
call pipe_compare_sym1(rm, ip,'ad:16:fln ')
endif
!
! --- rhs: flx, fly, rp+, rm+
! --- lhs: flx, fly
!
margin = mbdy_a - 4
!
!$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
! --- compare two model runs.
call pipe_compare_sym2(flx, iu,'ad:18:flx ', &
fly, iv,'ad:18:fly ')
endif
!
!diag i=itests
!diag j=jtests
!diag write (lp,'(''advem (2)'',2i6,f22.3/1pe39.2/0pf21.3,1pe9.2,0pf9.3, &
!diag 1pe9.2,0pf9.3/1pe39.2/0pf39.3)') i,j,fldlo(i-1,j),u(i,j),fldlo(i,j-1), &
!diag v(i,j),fldlo(i,j),v(i,j+1),fldlo(i,j+1),u(i+1,j),fldlo(i+1,j)
!
! --- rhs: flx+, fly+, fldlo, fcn, fmx
! --- lhs: flxdiv, fld
!
margin = mbdy_a - 5
!
!$OMP PARALLEL DO PRIVATE(j,i) &
!$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)
!
!...........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
!
fldan(i,j) = fld(i,j)*fcn(i,j)*scal(i,j)
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
! --- compare two model runs.
call pipe_compare_sym1(flxdiv, ip,'ad:620:flxdv')
call pipe_compare_sym1(fld, ip,'ad:1620:fld ')
endif
return
end subroutine advem_mpdata
subroutine advem_pcm(fld,u,v,fco,fcn,scal,scali,dt2)
implicit none
!
real, intent(in) :: dt2
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
intent(inout) :: fld
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
intent(in) :: u,v,scal,scali,fco,fcn
!
! Piecewise Constant Method (Donor Cell, Upwind)
! Over two time steps (may require half the normal time step for stability).
!
! time steps are "old", "center" and "new".
!
! fld - scalar field, need not be >0, old input but new output
! u,v - mass fluxes satisfying continuity equation (old to new)
! fco - thickness of the layer at old time step
! fcn - thickness of the layer at new time step
! scal - spatial increments (squared)
! scali - inverse of scal
! dt2 - temporal increment (from old to new)
!
! on return, fld's valid halo will be 0 wide.
!
real, parameter :: onemu=9806.e-12 !very small layer thickness
!
real q
integer i,j,l,ia,ib,ja,jb,mbdy_a,margin
!
! --- rhs: u, v, fld+
! --- lhs: flx, fly
!
mbdy_a = mbdy_advtyp(0) ! = 2
!
margin = mbdy_a - 1
!
!$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
!
if (lpipe .and. lpipe_advem) then
! --- compare two model runs.
call pipe_compare_sym2(flx, iu,'ad:11:flx ', &
fly, iv,'ad:11:fly ')
endif
!
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
!
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
! --- compare two model runs.
call pipe_compare_sym2(flx, iu,'ad:22:flx ', &
fly, iv,'ad:33:fly ')
endif
!diag if (itests.gt.0 .and. jtests.gt.0) then
!diag i=itests
!diag j=jtests
!diag write (lp,'(a,2i6,f22.3/1pe39.2/0pf21.3,1pe9.2,0pf9.3, &
!diag 1pe9.2,0pf9.3/1pe39.2/0pf39.3)') &
!diag 'advem (1)',i+i0,j+j0, &
!diag fld(i-1,j),u(i,j),fld(i,j-1),v(i,j), &
!diag fld(i,j),v(i,j+1),fld(i,j+1),u(i+1,j),fld(i+1,j)
!diag endif
!
! --- rhs: flx+, fly+, fld, fco, fcn
! --- lhs: flxdiv, fld
!
margin = mbdy_a - 2
!
!$OMP PARALLEL DO PRIVATE(j,i,q) &
!$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)
!
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) ))
!
fldan(i,j) = fld( i,j)*fcn(i,j)*scal(i,j)
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
! --- compare two model runs.
call pipe_compare_sym1(fld, ip,'ad:610:fld ')
call pipe_compare_sym1(flxdiv, ip,'ad:610:flxdv')
endif
!
!diag i=itests
!diag j=jtests
!diag write (lp,'(''advem (2)'',2i6,f22.3/1pe39.2/0pf21.3,1pe9.2,0pf9.3, &
!diag 1pe9.2,0pf9.3/1pe39.2/0pf39.3)') i,j,fld(i-1,j),u(i,j),fld(i,j-1), &
!diag v(i,j),fld(i,j),v(i,j+1),fld(i,j+1),u(i+1,j),fld(i+1,j)
return
end subroutine advem_pcm
subroutine advem_fct2(fld,fldc,u,v,fco,fcn,scal,scali,dt2)
implicit none
!
real, intent(in) :: dt2
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
intent(inout) :: fld
real, dimension (1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
intent(in) :: fldc,u,v,scal,scali,fco,fcn
!
! Leapfrog 2nd order FCT
! S.T. Zalesak (1979): Fully multidimensional flux-corrected
! transport algorithms for fluids, J.Comput.Phys. 31 335-362.
!
! time steps are "old", "center" and "new".
!
! fld - scalar field, need not be >0, old input but new output
! fldc - scalar field at center time step
! u,v - mass fluxes satisfying continuity equation (old to new)
! fco - thickness of the layer at old time step
! fcn - thickness of the layer at new time step
! scal - spatial increments (squared)
! scali - inverse of scal
! dt2 - temporal increment (from old to new)
!
! on return, fld's valid halo will be 0 wide.
!
real, parameter :: onemu=9806.e-12 !very small layer thickness
!
real flxdn,flxdp,flydn,flydp,q
integer i,j,l,ia,ib,ja,jb,mbdy_a,margin
!
real :: fhx, fhy, fqmax, fqmin, famax, famin
real :: qdt2, qp, qm, fact
mbdy_a = mbdy_advtyp(2) ! = 5
!
! --- compute low-order and part of antidiffusive fluxes
!
! --- rhs: u, v, fld+
! --- lhs: flx, fly, fmx, fmn
!
margin = mbdy_a - 1
!
!$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
!
if (lpipe .and. lpipe_advem) then
! --- 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
!
if (ldebug_advem .and. itests.gt.0 .and. jtests.gt.0) then
i=itests
j=jtests
write (lp,'(a,2i6,3f10.5)') &
'advem: fld, rng ',i+i0,j+j0, &
fld(i,j),fmx(i,j),fmn(i,j)
endif
!
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
!
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
! --- compare two model runs.
call pipe_compare_sym2(flx, iu,'ad:22:flx ', &
fly, iv,'ad:33:fly ')
endif
!
!diag if (ldebug_advem .and. itests.gt.0 .and. jtests.gt.0) then
!diag i=itests
!diag j=jtests
!diag write (lp,'(a,2i6,f22.3/1pe39.2/0pf21.3,1pe9.2,0pf9.3, &
!diag 1pe9.2,0pf9.3/1pe39.2/0pf39.3)') &
!diag 'advem (1)',i+i0,j+j0, &
!diag fld(i-1,j),u(i,j),fld(i,j-1),v(i,j), &
!diag fld(i,j),v(i,j+1),fld(i,j+1),u(i+1,j),fld(i+1,j)
!diag endif
!
! --- rhs: flx+, fly+, fld, fmx, fmn, fco, fcn
! --- lhs: fldlo, fmxlo, fmnlo, flxdiv
!
margin = mbdy_a - 2
!
!$OMP PARALLEL DO PRIVATE(j,i,q) &
!$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
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
! --- compare two model runs.
call pipe_compare_sym1(fldlo, ip,'ad:610:fldlo')
call pipe_compare_sym1(flxdiv, ip,'ad:610:flxdv')
endif
!
if (ldebug_advem .and. itests.gt.0 .and. jtests.gt.0) then
i=itests
j=jtests
write (lp,'(a,2i6,3f10.5)') &
'advem: fldlo,rng ',i+i0,j+j0, &
fldlo(i,j),fmnlo(i,j),fmxlo(i,j)
endif
!
!.....Leapfrog step using high order scheme
!
! --- rhs: u, v, fld+, flx, fly
! --- lhs: fax, fay
!
margin = mbdy_a - 2
!
!$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
!
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
!========================================================
!
! --- finish computation of antidiffusive fluxes
!
! --- rhs: fmnlo+,fmxlo+,fax+,fay+,fldlo,fcn,scal
! --- lhs: rp, rm
!
margin = mbdy_a - 3
!
qdt2 = 1.0/dt2
!$OMP PARALLEL DO PRIVATE(j,i,ia,ib,ja,jb, &
!$OMP fqmax,fqmin,famax,famin,qp,qm) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
ia=ipim1(i,j) !i-1 if sea and i if land
ib=ipip1(i,j) !i+1 if sea and i if land
ja=ipjm1(i,j) !j-1 if sea and j if land
jb=ipjp1(i,j) !j+1 if sea and j if land
fqmax = max(fmxlo(i,j),fmxlo(ia,j),fmxlo(ib,j), &
fmxlo(i,ja),fmxlo(i,jb))
fqmin = min(fmnlo(i,j),fmnlo(ia,j),fmnlo(ib,j), &
fmnlo(i,ja),fmnlo(i,jb))
famax = max(0.0,fax(i, j) ) - min(0.0,fax(ib,j) ) + &
max(0.0,fay(i, j) ) - min(0.0,fay(i, jb))
famin = max(0.0,fax(ib,j) ) - min(0.0,fax(i, j) ) + &
max(0.0,fay(i, jb)) - min(0.0,fay(i, j) )
if (famax > 0.0) then
qp = (fqmax-fldlo(i,j)) *fcn(i,j)*scal(i,j)*qdt2
if (qp < famax) then
rp(i,j) = qp/famax !<1.0
else
rp(i,j) = 1.0
endif
else
rp(i,j) = 0.0
endif
if (famin > 0.0) then
qm = (fldlo(i,j)-fqmin) *fcn(i,j)*scal(i,j)*qdt2
if (qm < famin) then
rm(i,j) = qm/famin !<1.0
else
rm(i,j) = 1.0
endif
else
rm(i,j) = 0.0
endif
fmx(i,j) = fqmax !less restrictive maximum
fmn(i,j) = fqmin !less restrictive minimum
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
!
if (ldebug_advem .and. itests.gt.0 .and. jtests.gt.0) then
i=itests
j=jtests
write (lp,'(a,2i6,3f10.5)') &
'advem: fldc,rngfq',i+i0,j+j0, &
fldc(i,j),fmn(i,j),fmx(i,j)
endif
!
! --- rhs: rp+, rm+
! --- lhs: fax, fay
!
margin = mbdy_a - 4
!
!$OMP PARALLEL DO PRIVATE(j,i,fact) &
!$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
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
! --- compare two model runs.
call pipe_compare_sym2(flx, iu,'ad:18:flx ', &
fly, iv,'ad:18:fly ')
endif
!
!diag i=itests
!diag j=jtests
!diag write (lp,'(''advem (2)'',2i6,f22.3/1pe39.2/0pf21.3,1pe9.2,0pf9.3, &
!diag 1pe9.2,0pf9.3/1pe39.2/0pf39.3)') i,j,fldlo(i-1,j),u(i,j),fldlo(i,j-1), &
!diag v(i,j),fldlo(i,j),v(i,j+1),fldlo(i,j+1),u(i+1,j),fldlo(i+1,j)
!
! --- rhs: fax+, fay+, fld, fcn, fmx, fmn
! --- lhs: fld
!
margin = mbdy_a - 5
!
!$OMP PARALLEL DO PRIVATE(j,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
fldao(i,j) = fld(i,j)*fco(i,j)*scal(i,j)
!
!...........apply antidiffusive flux correction
flxdiv(i,j)=((fax(i+1,j)-fax(i,j))+ &
(fay(i,j+1)-fay(i,j)) )*dt2*scali(i,j)
!max,min should only be active for very thin layers
fld(i,j)=max( fmn(i,j), min( fmx(i,j), &
fldlo(i,j)-flxdiv(i,j)/(fcn(i,j)+onemu) ))
!
fldan(i,j) = fld(i,j)*fcn(i,j)*scal(i,j)
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
if (lpipe .and. lpipe_advem) then
! --- compare two model runs.
call pipe_compare_sym1(flxdiv, ip,'ad:620:flxdv')
call pipe_compare_sym1(fld, ip,'ad:1620:fld ')
endif
!
if (ldebug_advem .and. itests.gt.0 .and. jtests.gt.0) then
i=itests
j=jtests
write (lp,'(a,2i6,f10.5)') &
'advem: fld ',i+i0,j+j0, &
fld(i,j)
endif
return
end subroutine advem_fct2
subroutine advem_fct2c(fld,fldc,u,v,fco,fcn, scal,scali,dt2)
implicit none