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cnuity.F90
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cnuity.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
subroutine cnuity(m,n)
use mod_xc ! HYCOM communication interface
use mod_cb_arrays ! HYCOM saved arrays
use mod_pipe ! HYCOM debugging interface
use mod_floats ! HYCOM synthetic floats, drifters and moorings
#if defined(STOKES)
use mod_stokes ! HYCOM Stokes drift
#endif
!
! --- hycom version 1.0
implicit none
!
integer m,n
!
! --- ------------------------------------------------------
! --- continuity equation (flux-corrected transport version)
! --- ------------------------------------------------------
! --- on entry:
! --- dp( :,:,:,n) = time step t-1
! --- dp( :,:,:,m) = time step t
!
! --- dpv( :,:,:,n) = time step t-1
! --- dpv( :,:,:,m) = time step t
! --- dpu( :,:,:,n) = time step t-1
! --- dpu( :,:,:,m) = time step t
!
! --- on exit:
! --- dpo(:,:,:,n) = time step t-1
! --- dpo(:,:,:,m) = time step t
! --- dp( :,:,:,m) = time step t with RA time smoothing
! --- dp( :,:,:,n) = time step t+1
!
! --- onetacnt(:,:) = 1+eta afer cnuity
! --- ------------------------------------------------------
!
logical, parameter :: lpipe_cnuity=.true. !usually .false.
!
real, parameter :: dpfatal=-10.0 !fatal negative dp in meters
real, parameter :: epsil_cnuity=1.e-14
!
#if defined(RELO)
integer, save, allocatable, dimension (:,:) :: &
masku,maskv
real, save, allocatable, dimension (:,:) :: &
pold,oneta_u,oneta_v
real, save, allocatable, dimension (:) :: &
dpmn
#else
integer, save, dimension(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) :: &
masku,maskv
real, save, dimension(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) :: &
pold,oneta_u,oneta_v
real, save, dimension(1-nbdy:jdm+nbdy) :: &
dpmn
#endif
!
integer i,iflip,iprint,isave,j,jsave,k,l,ia,ib,ja,jb,margin,mbdy
real q,dpmin,clip,flxhi,flxlo,dtinv,dpup,dpdn,thkdfu,thkdfv
real dpold,dpmid,dpnew
real dpkmin(2*kdm)
!
character*12 text,textu,textv
!
#if defined(RELO)
if (.not.allocated(masku)) then
allocate( &
masku(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
maskv(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
pold(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
oneta_u(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy), &
oneta_v(1-nbdy:idm+nbdy,1-nbdy:jdm+nbdy) )
call mem_stat_add( 4*(idm+2*nbdy)*(jdm+2*nbdy) ) !real=2*int
masku = -99
maskv = -99
pold = r_init
oneta_u = r_init
oneta_v = r_init
allocate( &
dpmn(1-nbdy:jdm+nbdy) )
call mem_stat_add( jdm+2*nbdy )
dpmn = r_init
endif
!
#endif
mbdy = 6
!
call xctilr(dpmixl( 1-nbdy,1-nbdy, n),1, 1, 6,6, halo_ps)
call xctilr(dp( 1-nbdy,1-nbdy,1,1),1,2*kk, 6,6, halo_ps)
call xctilr(dpu( 1-nbdy,1-nbdy,1,m),1, kk, 6,6, halo_us)
call xctilr(dpv( 1-nbdy,1-nbdy,1,m),1, kk, 6,6, halo_vs)
call xctilr(u( 1-nbdy,1-nbdy,1,m),1, kk, 6,6, halo_uv)
call xctilr(v( 1-nbdy,1-nbdy,1,m),1, kk, 6,6, halo_vv)
call xctilr(ubavg( 1-nbdy,1-nbdy, m),1, 1, 6,6, halo_uv)
call xctilr(vbavg( 1-nbdy,1-nbdy, m),1, 1, 6,6, halo_vv)
!
! --- rhs: dpmixl.n
! --- lhs: util3, utotn, vtotn
!
margin = mbdy
!
!$OMP PARALLEL DO PRIVATE(j,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (btrmas) then
! --- use dp, rather than dp'
onetamas(i,j,:) = oneta(i,j,:)
if (SEA_U) then
! --- depthu is either pbot(i,j) or pbot(i-1,j)
if (pbot(i,j).eq.pbot(i-1,j)) then
oneta_u(i,j) = 0.5*(onetamas(i,j,m)+onetamas(i-1,j,m))
elseif (pbot(i,j).eq.depthu(i,j)) then
oneta_u(i,j) = onetamas(i,j,m)
else
oneta_u(i,j) = onetamas(i-1,j,m)
endif
endif !iu
if (SEA_V) then
! --- depthv is either pbot(i,j) or pbot(i,j-1)
if (pbot(i,j).eq.pbot(i,j-1)) then
oneta_v(i,j) = 0.5*(onetamas(i,j,m)+onetamas(i,j-1,m))
elseif (pbot(i,j).eq.depthv(i,j)) then
oneta_v(i,j) = onetamas(i,j,m)
else
oneta_v(i,j) = onetamas(i,j-1,m)
endif
endif !iv
else
! --- use dp'
onetamas(i,j,:) = 1.0
oneta_u(i,j) = 1.0
oneta_v(i,j) = 1.0
endif !btrmas:else
utotn(i,j) = 0.0
vtotn(i,j) = 0.0
util3(i,j) = 0.0
dpmold(i,j) = dpmixl(i,j,n) ! save for Robert-Asselin filter
do k= 1,kk
dpo(i,j,k,n) = dp(i,j,k,n) !t-1
enddo !k
enddo !i
enddo !j
!$OMP END PARALLEL DO
!
do 76 k=1,kk
!
! --- uflux/vflux = low-order (diffusive) mass fluxes at old time level.
! --- uflux2/vflux2 = 'antidiffusive' fluxes, defined as high-order minus low-
! --- order fluxes. high-order fluxes are second-order in space, time-centered.
!
! --- rhs: depthu+, util3, dp.n, ubavg.m
! --- lhs: uflux
!
margin = mbdy - 1
! write(6,*)'cnuity.F line 96'
!
do j=1-margin,jj+margin
do l=1,isu(j) !ok
i=ifu(j,l)-1
if (i.ge.1-margin) then
if (iuopn(i,j).ne.0) then
q=min(dp(i ,j,k,n),max(0.,depthu(i+1,j)-util3(i ,j))) &
* onetamas(i ,j,n)
utotm(i,j)=(u(i+1,j,k,m)+ubavg(i,j,m))*scuy(i,j)
#if defined(STOKES)
utotm(i,j)=utotm(i,j)+usd(i+1,j,k)*scuy(i,j)
#endif
uflux(i,j)=utotm(i,j)*q
endif
endif
i=ilu(j,l)+1
if (i.le.ii+margin) then
if (iuopn(i,j).ne.0) then
q=min(dp(i-1,j,k,n),max(0.,depthu(i-1,j)-util3(i-1,j))) &
* onetamas(i-1,j,n)
utotm(i,j)=(u(i-1,j,k,m)+ubavg(i,j,m))*scuy(i,j)
#if defined(STOKES)
utotm(i,j)=utotm(i,j)+usd(i-1,j,k)*scuy(i,j)
#endif
uflux(i,j)=utotm(i,j)*q
endif
endif
enddo
enddo
! write(6,*)'cnuity.F line 128'
!
! --- rhs: depthv+, util3, dp.n, vbavg.m
! --- lhs: vflux
!
margin = mbdy - 1
!
do i=1-margin,ii+margin
do l=1,jsv(i) !ok
j=jfv(i,l)-1
if (j.ge.1-margin) then
if (ivopn(i,j).ne.0) then
q=min(dp(i,j ,k,n),max(0.,depthv(i,j+1)-util3(i,j ))) &
* onetamas(i,j ,n)
vtotm(i,j)=(v(i,j+1,k,m)+vbavg(i,j,m))*scvx(i,j)
#if defined(STOKES)
vtotm(i,j)=vtotm(i,j)+vsd(i,j+1,k)*scvx(i,j)
#endif
vflux(i,j)=vtotm(i,j)*q
endif
endif
j=jlv(i,l)+1
if (j.le.jj+margin) then
if (ivopn(i,j).ne.0) then
q=min(dp(i,j-1,k,n),max(0.,depthv(i,j-1)-util3(i,j-1))) &
* onetamas(i,j-1,n)
vtotm(i,j)=(v(i,j-1,k,m)+vbavg(i,j,m))*scvx(i,j)
#if defined(STOKES)
vtotm(i,j)=vtotm(i,j)+vsd(i,j-1,k)*scvx(i,j)
#endif
vflux(i,j)=vtotm(i,j)*q
endif
endif
enddo
enddo
! write(6,*)'cnuity.F line 165'
!
! --- rhs: u.m, ubavg.m, depthu, dp.n+, util3+, dpu.m, uflux
! --- rhs: v.m, vbavg.m, depthv, dp.n+, util3+, dpv.m, vflux
! --- lhs: utotm,uflux,uflux2,uflx
! --- lhs: vtotm,vflux,vflux2,vflx
!
margin = mbdy - 1
!
!$OMP PARALLEL DO PRIVATE(j,i,q) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_U) then
utotm(i,j)=(u(i,j,k,m)+ubavg(i,j,m))*scuy(i,j)
#if defined(STOKES)
utotm(i,j)=utotm(i,j)+usd(i,j,k)*scuy(i,j)
#endif
if (utotm(i,j).ge.0.) then
q=min(dp(i-1,j,k,n),max(0.,depthu(i,j)-util3(i-1,j))) &
* onetamas(i-1,j,n)
else
q=min(dp(i ,j,k,n),max(0.,depthu(i,j)-util3(i ,j))) &
* onetamas(i ,j,n)
endif
uflux(i,j)=utotm(i,j)*q
uflux2(i,j)=utotm(i,j)*dpu(i,j,k,m)*oneta_u(i,j)- &
uflux(i,j)
uflx(i,j,k)=uflux(i,j)
endif !iu
enddo !i
!
! write(6,*)'cnuity.F line 197, j = ',j
do i=1-margin,ii+margin
if (SEA_V) then
vtotm(i,j)=(v(i,j,k,m)+vbavg(i,j,m))*scvx(i,j)
#if defined(STOKES)
vtotm(i,j)=vtotm(i,j)+vsd(i,j,k)*scvx(i,j)
#endif
if (vtotm(i,j).ge.0.) then
q=min(dp(i,j-1,k,n),max(0.,depthv(i,j)-util3(i,j-1))) &
* onetamas(i,j-1,n)
else
q=min(dp(i,j ,k,n),max(0.,depthv(i,j)-util3(i,j ))) &
* onetamas(i,j ,n)
endif
vflux(i,j)=vtotm(i,j)*q
vflux2(i,j)=vtotm(i,j)*dpv(i,j,k,m)*oneta_v(i,j)- &
vflux(i,j)
vflx(i,j,k)=vflux(i,j)
endif !iv
enddo !i
! write(6,*)'cnuity.F line 216, j = ',j
enddo !j
!$OMP END PARALLEL DO
! write(6,*)'cnuity.F line 216'
!
! --- advance -dp- field using low-order (diffusive) flux values
! --- rhs: dp.n, dp.m, util3, uflux+, vflux+
! --- lhs: dpo,util3,dp.n
!
margin = mbdy - 2
!
!$OMP PARALLEL DO PRIVATE(j,i,dpmin) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
dpmin=999.
do i=1-margin,ii+margin
if (SEA_P) then
util3(i,j)=util3(i,j)+dp(i,j,k,n)
dp(i,j,k,n)=dp(i,j,k,n)* &
onetamas(i,j,n)- &
((uflux(i+1,j)-uflux(i,j))+ &
(vflux(i,j+1)-vflux(i,j)))*delt1*scp2i(i,j)
dpo(i,j,k,m)=dp(i,j,k,n) ! save for loop 19 test
dpmin=min(dpmin,dp(i,j,k,n))
endif !ip
enddo !i
dpmn(j)=dpmin ! minimizes false sharing
enddo !j, loop 19
!$OMP END PARALLEL DO
!
dpmin=999.
do j=1,jj
dpmin=min(dpmin,dpmn(j))
enddo
dpkmin(k)=dpmin
!
if (lpipe .and. lpipe_cnuity) then
! --- compare two model runs.
write (text,'(a9,i3)') 'dp.low k=',k
call pipe_compare_sym1(dp(1-nbdy,1-nbdy,k,n),ip,text)
endif
!
do j=1-margin,jj+margin
do l=1,isu(j) !ok
i=ifu(j,l)-1
if (i.ge.1-margin) then
if (iuopn(i,j).ne.0) then
uflux(i,j)=0.0
endif
endif
i=ilu(j,l)+1
if (i.le.ii+margin) then
if (iuopn(i,j).ne.0) then
uflux(i,j)=0.0
endif
endif
enddo
enddo
!
do i=1-margin,ii+margin
do l=1,jsv(i) !ok
j=jfv(i,l)-1
if (j.ge.1-margin) then
if (ivopn(i,j).ne.0) then
vflux(i,j)=0.0
endif
endif
j=jlv(i,l)+1
if (j.le.jj+margin) then
if (ivopn(i,j).ne.0) then
vflux(i,j)=0.0
endif
endif
enddo
enddo
!
if (lpipe .and. lpipe_cnuity) then
! --- compare two model runs.
do j=1-margin,jj+margin
do i=1-margin,ii+margin
masku(i,j)=iu(i,j)
if (i.gt. 1) masku(i,j)=masku(i,j)+iu(i-1,j)
if (i.lt.ii) masku(i,j)=masku(i,j)+iu(i+1,j)
maskv(i,j)=iv(i,j)
if (j.gt. 1) maskv(i,j)=maskv(i,j)+iv(i,j-1)
if (j.lt.jj) maskv(i,j)=maskv(i,j)+iv(i,j+1)
enddo
enddo
write (textu,'(a9,i3)') 'uflux k=',k
write (textv,'(a9,i3)') 'vflux k=',k
call pipe_compare_sym2(uflux,masku,textu, &
vflux,maskv,textv)
write (textu,'(a9,i3)') 'uflux2 k=',k
write (textv,'(a9,i3)') 'vflux2 k=',k
call pipe_compare_sym2(uflux2,masku,textu, &
vflux2,maskv,textv)
endif
!
!diag if (mod(k,15).eq.1) then
!diag do i=itest-1,itest+1
!diag do j=jtest-1,jtest+1
!diag write (lp,101) nstep,i+i0,j+j0,k,dpo(i-1,j,k,n),uflux(i,j), &
!diag 'old dp''s, fluxes:',dpo(i,j-1,k,n),dpo(i,j,k,n),dpo(i,j+1,k,n) &
!diag ,vflux(i,j),dp(i,j,k,n),vflux(i,j+1),dpo(i+1,j,k,n),uflux(i+1,j)
!diag enddo
!diag enddo
!diag endif
101 format (i9,2i5,i3,1p,e15.2,e30.2/a17,6e10.2/e37.2,e30.2)
!
! --- at each grid point, determine the ratio of the largest permissible
! --- pos. (neg.) change in -dp- to the sum of all incoming (outgoing) fluxes
!
! --- rhs: dp.n+, uflux2+, vflux2+
! --- lhs: util1,util2
!
margin = mbdy - 2
!
!$OMP PARALLEL DO PRIVATE(j,i,ia,ib,ja,jb) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
! --- assume margin<nblk
ia=ipim1(i,j) !i-1 if sea and i if land
ib=ipip1(i,j) !i+1 if sea and i if land
ja=ipjm1(i,j) !j-1 if sea and j if land
jb=ipjp1(i,j) !j+1 if sea and j if land
util1(i,j)=max(dp(i,j,k,n),dp(ia,j,k,n),dp(ib,j,k,n), &
dp(i,ja,k,n),dp(i,jb,k,n))
util2(i,j)=max(0., &
min(dp(i,j,k,n),dp(ia,j,k,n),dp(ib,j,k,n), &
dp(i,ja,k,n),dp(i,jb,k,n)))
!
util1(i,j)=(util1(i,j)-dp(i,j,k,n)) &
/(((max(0.,uflux2(i,j))-min(0.,uflux2(i+1,j))) &
+(max(0.,vflux2(i,j))-min(0.,vflux2(i,j+1)))+epsil) &
*delt1*scp2i(i,j))
!
util2(i,j)=(util2(i,j)-dp(i,j,k,n)) &
/(((min(0.,uflux2(i,j))-max(0.,uflux2(i+1,j))) &
+(min(0.,vflux2(i,j))-max(0.,vflux2(i,j+1)))-epsil) &
*delt1*scp2i(i,j))
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
!
! --- limit antidiffusive fluxes
! --- (keep track in -utotn,vtotn- of discrepancy between high-order
! --- fluxes and the sum of low-order and clipped antidiffusive fluxes.
! --- this will be used later to restore nondivergence of barotropic flow)
!
! --- rhs: uflux2+,util1+,util2+
! --- rhs: vflux2+,util1+,util2+
! --- lhs: utotn,uflux,uflx
! --- lhs: vtotn,vflux,vflx
!
margin = mbdy - 3
!
!$OMP PARALLEL DO PRIVATE(j,i,clip) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_U) then
if (uflux2(i,j).ge.0.) then
clip=min(1.,util1(i,j),util2(i-1,j))
else
clip=min(1.,util2(i,j),util1(i-1,j))
endif
utotn(i,j)=utotn(i,j)+uflux2(i,j)*(1.-clip)
uflux(i,j)=uflux2(i,j)*clip
uflx(i,j,k)=uflx(i,j,k)+uflux(i,j)
endif !iu
enddo !i
!
do i=1-margin,ii+margin
if (SEA_V) then
if (vflux2(i,j).ge.0.) then
clip=min(1.,util1(i,j),util2(i,j-1))
else
clip=min(1.,util2(i,j),util1(i,j-1))
endif
vtotn(i,j)=vtotn(i,j)+vflux2(i,j)*(1.-clip)
vflux(i,j)=vflux2(i,j)*clip
vflx(i,j,k)=vflx(i,j,k)+vflux(i,j)
endif !iv
enddo !i
enddo !j
!$OMP END PARALLEL DO
!
! --- evaluate effect of antidiffusive fluxes on -dp- field
!
! --- rhs: dp.n, p, uflux+,vflux+
! --- lhs: dp.n, p
!
margin = mbdy - 4
!
!$OMP PARALLEL DO PRIVATE(j,i,dpmin) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
dpmin=999.
do i=1-margin,ii+margin
if (SEA_P) then
dp(i,j,k,n)=dp(i,j,k,n)- &
((uflux(i+1,j)-uflux(i,j))+ &
(vflux(i,j+1)-vflux(i,j)))*delt1*scp2i(i,j)
p(i,j,k+1)=p(i,j,k)+dp(i,j,k,n)
dpmin=min(dpmin,dp(i,j,k,n))
endif !ip
enddo !i
dpmn(j)=dpmin ! minimizes false sharing
enddo !j, loop 15
!$OMP END PARALLEL DO
!
dpmin=999.
do j=1,jj
dpmin=min(dpmin,dpmn(j))
enddo
dpkmin(k+kk)=dpmin
!
if (lpipe .and. lpipe_cnuity) then
! --- compare two model runs.
write (text,'(a9,i3)') 'dp-dif k=',k
call pipe_compare_sym1(dp(1-nbdy,1-nbdy,k,n),ip,text)
endif
!
76 continue ! k=1,kk
!
! --- check for negative thicknesses.
!
100 format (i9,' i,j,k=',2i5,i3,' neg. dp (m) in loop ',i2,g15.2,a)
!
if (mod(nstep,3).eq.0) then !skip some time steps for efficiency
call xcminr(dpkmin(1:2*kk))
do k= 1,kk
dpmin=dpkmin(k)
if ((k.eq.1 .and. dpmin.le.0.0) .or. dpmin.lt.-onecm) then
iprint = 0
do j=1,jj
do i=1,ii
if (SEA_P) then
if (dpo(i,j,k,m).eq.dpmin .and. iprint.le.5) then
write (lp,100) nstep,i+i0,j+j0,k,19, &
dpmin*qonem,' max'
iprint = iprint + 1
endif
endif !ip
enddo !i
enddo !j
call xcsync(flush_lp)
if (dpmin.lt.dpfatal*onem) then
do j=1,jj
do i=1,ii
if (SEA_P) then
if (dpo(i,j,k,m).lt.dpfatal*onem .and. &
iprint.le.5) then
write (lp,100) nstep,i+i0,j+j0,k,19, &
dpo(i,j,k,m)*qonem,' fatal'
iprint = iprint + 1
endif
endif !ip
enddo !i
enddo !j
call xcsync(flush_lp)
endif !dpfatal
endif
enddo !k
do k= 1,kk
dpmin=dpkmin(k+kk)
if ((k.eq.1 .and. dpmin.le.0.0) .or. dpmin.lt.-onecm) then
iprint = 0
do j=1,jj
do i=1,ii
if (SEA_P) then
if (dp(i,j,k,n).eq.dpmin .and. iprint.le.5) then
write (lp,100) nstep,i+i0,j+j0,k,15, &
dpmin*qonem,' max'
iprint = iprint + 1
endif
endif !ip
enddo !i
enddo !j
call xcsync(flush_lp)
if (dpmin.lt.dpfatal*onem) then
do j=1,jj
do i=1,ii
if (SEA_P) then
if (dp(i,j,k,n).lt.dpfatal*onem .and. &
iprint.le.5) then
write (lp,100) nstep,i+i0,j+j0,k,15, &
dp(i,j,k,n)*qonem,' fatal'
iprint = iprint + 1
endif
endif !ip
enddo !i
enddo !j
call xcsync(flush_lp)
endif !dpfatal
endif
enddo !k
if (minval(dpkmin(1:2*kk)).lt.dpfatal*onem) then
if (mnproc.eq.1) then
write(lp,'(/ a,f9.2 /)') &
'error: neg. dp (m) < ',dpfatal
! write(lp,*) 'dpkmin =',qonem*dpkmin(1:2*kk)
endif
call xcstop('cnuity')
stop 'cnuity'
endif !dpfatal
endif !every 3 time steps
!
if (.not.btrmas) then
!
! --- restore nondivergence of vertically integrated mass flow by
! --- recovering fluxes lost in the flux limiting process.
! --- treat these fluxes as an 'upstream' barotropic correction to
! --- the sum of diffusive and antidiffusive fluxes obtained so far.
!
do 77 k=1,kk
!
! --- rhs: utotn, dp.n+, p+
! --- rhs: vtotn, dp.n+, p+
! --- lhs: uflux, uflx
! --- lhs: vflux, vflx
!
margin = mbdy - 5
!
!$OMP PARALLEL DO PRIVATE(j,i,q) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_U) then
if (utotn(i,j).ge.0.) then
! if (p(i-1,j,kk+1).eq.0.0) then
! write(lp,*) 'error: i,j,p.i-1 = ',
! & i,j,p(i-1,j,kk+1)
! call xcstop('(cnuity)')
! stop
! endif
q=dp(i-1,j,k,n)/p(i-1,j,kk+1)
else
! if (p(i, j,kk+1).eq.0.0) then
! write(lp,*) 'error: i,j,p.i = ',
! & i,j,p(i, j,kk+1)
! call xcstop('(cnuity)')
! stop
! endif
q=dp(i ,j,k,n)/p(i ,j,kk+1)
endif
uflux(i,j)=utotn(i,j)*q
uflx(i,j,k)=uflx(i,j,k)+uflux(i,j)
endif !iu
enddo !i
!
do i=1-margin,ii+margin
if (SEA_V) then
if (vtotn(i,j).ge.0.) then
! if (p(i,j-1,kk+1).eq.0.0) then
! write(lp,*) 'error: i,j,p.j-1 = ',
! & i,j,p(i,j-1,kk+1)
! call xcstop('(cnuity)')
! stop
! endif
q=dp(i,j-1,k,n)/p(i,j-1,kk+1)
else
! if (p(i,j, kk+1).eq.0.0) then
! write(lp,*) 'error: i,j,p.j = ',
! & i,j,p(i,j, kk+1)
! call xcstop('(cnuity)')
! stop
! endif
q=dp(i,j ,k,n)/p(i,j ,kk+1)
endif
vflux(i,j)=vtotn(i,j)*q
vflx(i,j,k)=vflx(i,j,k)+vflux(i,j)
endif !iv
enddo !i
enddo !j
!$OMP END PARALLEL DO
!
! --- rhs: dp.n, p, uflux+, vflux+
! --- lhs: dp.n, p
!
margin = mbdy - 6
!
!$OMP PARALLEL DO PRIVATE(j,i,dpmin) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
dpmin=999.
do i=1-margin,ii+margin
if (SEA_P) then
dp( i,j,k,n)=dp(i,j,k,n)- &
((uflux(i+1,j)-uflux(i,j))+ &
(vflux(i,j+1)-vflux(i,j)))*delt1*scp2i(i,j)
p(i,j,k+1)=p(i,j,k)+dp(i,j,k,n)
dpmin=min(dpmin,dp(i,j,k,n))
endif !ip
enddo !i
dpmn(j)=dpmin ! minimizes false sharing
enddo !j, loop 14
!
dpmin=999.
do j=1,jj
dpmin=min(dpmin,dpmn(j))
enddo
dpkmin(k)=dpmin
!
if (lpipe .and. lpipe_cnuity) then
! --- compare two model runs.
write (text,'(a9,i3)') 'dp.res k=',k
call pipe_compare_sym1(dp(1-nbdy,1-nbdy,k,n),ip,text)
endif
!
77 continue ! k=1,kk
!
call pipe_comparall(m,n, 'cnui77, step')
!
endif !.not.btrmas
!
! --- check for negative thicknesses.
!
if (mod(nstep,3).eq.0) then !skip some time steps for efficiency
call xcminr(dpkmin(1:kk))
do k= 1,kk
dpmin=dpkmin(k)
if (dpmin.lt.-onecm) then
do j=1,jj
do i=1,ii
if (SEA_P) then
if (dp(i,j,k,n).eq.dpmin) then
write (lp,100) nstep,i+i0,j+j0,k,14, &
dpmin*qonem,' max'
endif
endif !ip
enddo !i
enddo !j
call xcsync(flush_lp)
endif
enddo !k
endif !every 3 time steps
!
if (.not.btrmas) then
!
! --- add bottom-pressure restoring term arising from split-explicit treatment
! --- of continuity equation (step 4 in appendix b to 1992 brhs paper)
!
! --- rhs: dp.n, p, pbot
! --- lhs: dp.n, p, dpmixl.n
!
margin = mbdy - 6
!
!$OMP PARALLEL DO PRIVATE(j,k,i,q) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
q = pbot(i,j)/p(i,j,kk+1)
do k=1,kk
dp(i,j,k,n)=dp(i,j,k,n)*q
p(i,j,k+1)=p(i,j,k)+dp(i,j,k,n)
enddo !k
if (isopyc) then
dpmixl(i,j,n)=dp(i,j,1,n)
endif
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
!
if (lpipe .and. lpipe_cnuity) then
! --- compare two model runs.
do k=1,kk
write (text,'(a9,i3)') 'dp.bot k=',k
call pipe_compare_sym1(dp(1-nbdy,1-nbdy,k,n),ip,text)
enddo
endif
!
endif !.not.btrmas
!
! --- ---------------------------------------------------------------------
! --- biharmonic thickness diffusion (literally, interface depth diffusion)
! --- ---------------------------------------------------------------------
!
if (thkdf4.eq.0.) go to 800 ! only one of thkdf2 and thkdf4 is non-zero
! apply thkdf4
!
mbdy = 6
!
call xctilr(dpmixl( 1-nbdy,1-nbdy, n),1, 1, 6,6, halo_ps)
call xctilr(dp( 1-nbdy,1-nbdy,1,n),1,kk, 6,6, halo_ps)
call xctilr(p( 1-nbdy,1-nbdy,2 ),1,kk, 6,6, halo_ps)
!
dtinv=1./delt1
iflip=mod(nstep,2)
!
! --- rhs: p
! --- lhs: uflux, vflux, pold
!
margin = mbdy
!
!$OMP PARALLEL DO PRIVATE(j,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_U) then
uflux(i,j)=0.
endif !iu
if (SEA_V) then
vflux(i,j)=0.
endif !iv
if (SEA_P) then
if (iflip.eq.1) then
pold(i,j)=p(i,j,kk+1)
else
pold(i,j)=0.
endif
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
!
! --- alternate between upward and downward direction in k loop
!
do 13 k=2*(1-iflip)+kk*iflip,kk*(1-iflip)+2*iflip,1-2*iflip
!
! --- rhs: p+, dp.n+
! --- lhs: util1, util2
!
margin = mbdy - 1
!
!$OMP PARALLEL DO PRIVATE(j,i,ia,ib,ja,jb) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
if (min(dp(i,j,k,n),dp(i,j,k-1,n)).lt.onecm) then
util1(i,j)=0.0
util2(i,j)=0.0
else
ia=ipim1x(i,j) !i-1 if sea; else i+1 if sea; otherwise i
ib=ipip1x(i,j) !i+1 if sea; else i-1 if sea; otherwise i
ja=ipjm1x(i,j) !j-1 if sea; else j+1 if sea; otherwise j
jb=ipjp1x(i,j) !j+1 if sea; else j-1 if sea; otherwise j
util1(i,j)=p(i,j,k)-.5*(p(ia,j,k)+p(ib,j,k))
util2(i,j)=p(i,j,k)-.5*(p(i,ja,k)+p(i,jb,k))
if (util1(i,j).gt.0.0) then
if (min(dp(ia,j,k, n),dp(ib,j,k, n)).lt.onecm) then
util1(i,j)=0.0
endif
else
if (min(dp(ia,j,k-1,n),dp(ib,j,k-1,n)).lt.onecm) then
util1(i,j)=0.0
endif
endif
if (util2(i,j).gt.0.0) then
if (min(dp(i,ja,k, n),dp(i,jb,k, n)).lt.onecm) then
util2(i,j)=0.0
endif
else
if (min(dp(i,ja,k-1,n),dp(i,jb,k-1,n)).lt.onecm) then
util2(i,j)=0.0
endif
endif
endif !min(dp):else
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
!
! --- limit fluxes to avoid intertwining interfaces
!
! --- rhs: p+, pold+, uflux, util1+, uflx+
! --- rhs: p+, pold+, vflux, util2+, vflx+
! --- lhs: uflux, uflx+
! --- lhs: vflux, vflx+
!
margin = mbdy - 2
!
!$OMP PARALLEL DO PRIVATE(j,i,flxhi,flxlo,thkdfu,thkdfv) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
!
do i=1-margin,ii+margin
if (SEA_U) then
flxhi= .25*(p(i ,j,kk+1)-p(i ,j,k))*scp2(i ,j)
flxlo=-.25*(p(i-1,j,kk+1)-p(i-1,j,k))*scp2(i-1,j)
!
if (iflip.eq.0) then ! downward k loop
flxhi=min(flxhi, &
uflux(i,j)+ &
.25*(p(i-1,j,k)-pold(i-1,j))*scp2(i-1,j))
flxlo=max(flxlo, &
uflux(i,j)- &
.25*(p(i ,j,k)-pold(i ,j))*scp2(i ,j))
else ! upward k loop
flxhi=min(flxhi, &
uflux(i,j)+ &
.25*(pold(i ,j)-p(i ,j,k))*scp2(i ,j))
flxlo=max(flxlo, &
uflux(i,j)- &
.25*(pold(i-1,j)-p(i-1,j,k))*scp2(i-1,j))
endif
!
thkdfu = delt1*thkdf4u(i,j)
uflux(i,j)=min( flxhi, &
max( flxlo, &
thkdfu* &
(util1(i-1,j)-util1(i,j)) ) )
uflx(i,j,k-1)=uflx(i,j,k-1)+uflux(i,j)*dtinv
uflx(i,j,k )=uflx(i,j,k )-uflux(i,j)*dtinv
endif !iu
enddo !i
!
do i=1-margin,ii+margin
if (SEA_V) then
flxhi= .25*(p(i,j ,kk+1)-p(i,j ,k))*scp2(i,j )
flxlo=-.25*(p(i,j-1,kk+1)-p(i,j-1,k))*scp2(i,j-1)
!
if (iflip.eq.0) then ! downward k loop
flxhi=min(flxhi, &
vflux(i,j)+ &
.25*(p(i,j-1,k)-pold(i,j-1))*scp2(i,j-1))
flxlo=max(flxlo, &
vflux(i,j)- &
.25*(p(i,j ,k)-pold(i,j ))*scp2(i,j ))
else ! upward k loop
flxhi=min(flxhi, &
vflux(i,j)+ &
.25*(pold(i,j )-p(i,j ,k))*scp2(i,j ))
flxlo=max(flxlo, &
vflux(i,j)- &
.25*(pold(i,j-1)-p(i,j-1,k))*scp2(i,j-1))
endif
!
thkdfv = delt1*thkdf4v(i,j)
vflux(i,j)=min( flxhi, &
max( flxlo, &
thkdfv* &
(util2(i,j-1)-util2(i,j)) ) )
vflx(i,j,k-1)=vflx(i,j,k-1)+vflux(i,j)*dtinv
vflx(i,j,k )=vflx(i,j,k )-vflux(i,j)*dtinv
endif !iv
enddo !i
enddo !j
!$OMP END PARALLEL DO
!
! --- rhs: p, uflux+, vflux+
! --- lhs: pold, p
!
margin = mbdy - 2
!
!$OMP PARALLEL DO PRIVATE(j,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do i=1-margin,ii+margin
if (SEA_P) then
pold(i,j)=p(i,j,k)
p(i,j,k)=p(i,j,k)-((uflux(i+1,j)-uflux(i,j))+ &
(vflux(i,j+1)-vflux(i,j)))*scp2i(i,j)
endif !ip
enddo !i
enddo !j
!$OMP END PARALLEL DO
!
!diag if (itest.gt.0.and.jtest.gt.0) &
!diag write (lp,'(i9,2i5,i3,'' intfc.depth diffusion -- p_old,p_new ='', &
!diag 2f9.3)') nstep,itest,jtest,k,pold(itest,jtest)*qonem,p(itest, &
!diag jtest,k)*qonem
!
13 continue ! k=2*(1-iflip)+kk*iflip,kk*(1-iflip)+2*iflip,1-2*iflip
!
! --- rhs: p
! --- lhs: p, dp.n, dpmixl.n
!
margin = mbdy - 2
!
!$OMP PARALLEL DO PRIVATE(j,k,i) &
!$OMP SCHEDULE(STATIC,jblk)
do j=1-margin,jj+margin
do k=1,kk
do i=1-margin,ii+margin
if (SEA_P) then
if (p(i,j,k+1).lt.p(i,j,k)) then
!diag write (lp,'(i9,2i5,i3,a,g15.2,i4)') nstep,i+i0,j+j0,k, &
!diag ' neg. dp after thknss smoothing', &
!diag qonem*(p(i,j,k+1)-p(i,j,k)),iflip
p(i,j,k+1)=p(i,j,k)
endif
dp(i,j,k,n)=p(i,j,k+1)-p(i,j,k)
if (isopyc .and. k.eq.1) then
dpmixl(i,j,n)=dp(i,j,k,n)
endif
endif !ip
enddo !i
enddo !k
enddo !j
!$OMP END PARALLEL DO
!
if (lpipe .and. lpipe_cnuity) then
! --- compare two model runs.
do k=1,kk
write (text,'(a9,i3)') 'dp-df4 k=',k
call pipe_compare_sym1(dp(1-nbdy,1-nbdy,k,n),ip,text)
enddo
endif
!
800 continue ! end of biharmonic thickness diffusion
!
! --- ---------------------------------------------------------------------
! --- Laplacian thickness diffusion (literally, interface depth diffusion)
! --- ---------------------------------------------------------------------
!
if (thkdf2.eq.0.) go to 850 ! only one of thkdf2 and thkdf4 is non-zero
! apply thkdf2
!
mbdy = 6