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SIS_tracer_advect.F90
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module SIS_tracer_advect
!***********************************************************************
!* GNU General Public License *
!* This file is a part of SIS2. *
!* *
!* SIS2 is free software; you can redistribute it and/or modify it and *
!* are expected to follow the terms of the GNU General Public License *
!* as published by the Free Software Foundation; either version 2 of *
!* the License, or (at your option) any later version. *
!* *
!* SIS2 is distributed in the hope that it will be useful, but WITHOUT *
!* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY *
!* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public *
!* License for more details. *
!* *
!* For the full text of the GNU General Public License, *
!* write to: Free Software Foundation, Inc., *
!* 675 Mass Ave, Cambridge, MA 02139, USA. *
!* or see: http://www.gnu.org/licenses/gpl.html *
!***********************************************************************
!********+*********+*********+*********+*********+*********+*********+**
!* *
!* By Robert Hallberg, 1996 - 2012, adapted for SIS2 in 2014-2016. *
!* *
!* This program contains the subroutines that advect tracers *
!* horizontally (i.e. along layers). This code was modified from the *
!* corresponding MOM6 / GOLD code to work with the snow and ice *
!* tracers of SIS2. *
!* *
!* advect_SIS_tracers advects tracer concentrations using the *
!* modified flux advection scheme from Easter (Mon. Wea. Rev., 1993) *
!* with tracer distributions that are piecewise constant, *
!* piecewise linear (given by the monotonic scheme proposed by *
!* Lin et al. (Mon. Wea. Rev., 1994)), or the montonic piecewise *
!* parabolic method, as described in Carpenter et al. (MWR, 1990). *
!* This detects the mass of ice or snow in a grid cell and thickness *
!* category at the previous instance when the tracer concentration *
!* was changed is consistent with the mass fluxes and the new masses. *
!* *
!* A small fragment of the grid is shown below: *
!* *
!* j+1 x ^ x ^ x At x: q *
!* j+1 > o > o > At ^: v, vh *
!* j x ^ x ^ x At >: u, uh *
!* j > o > o > At o: tr, h *
!* j-1 x ^ x ^ x *
!* i-1 i i+1 At x & ^: *
!* i i+1 At > & o: *
!* *
!* The boundaries always run through q grid points (x). *
!* *
!********+*********+*********+*********+*********+*********+*********+**
use MOM_cpu_clock, only : cpu_clock_id, cpu_clock_begin, cpu_clock_end
use MOM_cpu_clock, only : CLOCK_MODULE, CLOCK_ROUTINE
use SIS_diag_mediator, only : post_SIS_data, query_SIS_averaging_enabled, SIS_diag_ctrl
use SIS_diag_mediator, only : register_SIS_diag_field, safe_alloc_ptr, time_type
use MOM_domains, only : pass_var, pass_vector, sum_across_PEs, max_across_PEs
use MOM_error_handler, only : SIS_error=>MOM_error, FATAL, WARNING, SIS_mesg=>MOM_mesg
use MOM_file_parser, only : get_param, log_version, param_file_type
use SIS_hor_grid, only : SIS_hor_grid_type
use ice_grid, only : ice_grid_type
use SIS_tracer_registry, only : SIS_tracer_registry_type, SIS_tracer_type, SIS_tracer_chksum
implicit none ; private
#include <SIS2_memory.h>
public advect_SIS_tracers, advect_tracers_thicker, advect_scalar
public SIS_tracer_advect_init, SIS_tracer_advect_end
type, public :: SIS_tracer_advect_CS ; private
real :: dt ! The baroclinic dynamics time step, in s.
type(SIS_diag_ctrl), pointer :: diag ! A structure that is used to regulate the
! timing of diagnostic output.
logical :: debug ! If true, write verbose checksums for debugging purposes.
logical :: use_upwind2d ! If true, use the non-split upwind scheme that was
! was used in older versions of SIS.
logical :: usePPM ! If true, use PPM tracer advection instead of PLM.
logical :: usePCM ! If true, use PCM tracer advection instead of PLM.
end type SIS_tracer_advect_CS
logical :: first_call = .true.
integer :: id_clock_advect, id_clock_pass, id_clock_sync
contains
subroutine advect_SIS_tracers(h_prev, h_end, uhtr, vhtr, dt, G, IG, CS, TrReg, snow_tr ) ! (, OBC)
type(SIS_hor_grid_type), intent(inout) :: G
type(ice_grid_type), intent(inout) :: IG
real, dimension(SZI_(G),SZJ_(G),SZCAT_(IG)), intent(in) :: h_prev, h_end
real, dimension(SZIB_(G),SZJ_(G),SZCAT_(IG)), intent(in) :: uhtr
real, dimension(SZI_(G),SZJB_(G),SZCAT_(IG)), intent(in) :: vhtr
real, intent(in) :: dt
type(SIS_tracer_advect_CS), pointer :: CS
type(SIS_tracer_registry_type), pointer :: TrReg
logical, intent(in) :: snow_tr
! Arguments: h_prev - Category thickness times fractional coverage before advection, in m or kg m-2.
! (in) h_end - Layer thickness times fractional coverage after advection, in m or kg m-2.
! (in) uhtr - Accumulated volume or mass fluxes through zonal faces,
! in m3 s-1 or kg s-1.
! (in) vhtr - Accumulated volume or mass fluxes through meridional faces,
! in m3 s-1 or kg s-1.
!! (in) OBC - This open boundary condition type specifies whether, where,
!! and what open boundary conditions are used.
! (in) dt - Time increment in s.
! (in) G - The ocean's grid structure.
! (in) IG - The sea-ice-specific grid structure.
! (in) CS - The control structure returned by a previous call to
! SIS_tracer_advect_init.
! (in) TrReg - A pointer to the tracer registry.
! (in) snow_tr - If true, advect the snow tracers, otherwise advect the
! ice tracers.
integer ntr
if (.not. associated(CS)) call SIS_error(FATAL, "SIS_tracer_advect: "// &
"SIS_tracer_advect_init must be called before advect_tracer.")
if (.not. associated(TrReg)) call SIS_error(FATAL, "SIS_tracer_advect: "// &
"register_tracer must be called before advect_tracer.")
ntr = TrReg%ntr
if (ntr==0) return
call cpu_clock_begin(id_clock_advect)
if (snow_tr) then
if (CS%use_upwind2d) then
call advect_upwind_2d(TrReg%Tr_snow, h_prev, h_end, uhtr, vhtr, ntr, dt, G, IG)
else
call advect_tracer(TrReg%Tr_snow, h_prev, h_end, uhtr, vhtr, ntr, dt, G, IG, CS)
endif
else
if (CS%use_upwind2d) then
call advect_upwind_2d(TrReg%Tr_ice, h_prev, h_end, uhtr, vhtr, ntr, dt, G, IG)
else
call advect_tracer(TrReg%Tr_ice, h_prev, h_end, uhtr, vhtr, ntr, dt, G, IG, CS)
endif
endif
call cpu_clock_end(id_clock_advect)
end subroutine advect_SIS_tracers
subroutine advect_tracer(Tr, h_prev, h_end, uhtr, vhtr, ntr, dt, G, IG, CS) ! (, OBC)
type(SIS_tracer_type), dimension(ntr), intent(inout) :: Tr
type(SIS_hor_grid_type), intent(inout) :: G
type(ice_grid_type), intent(inout) :: IG
real, dimension(SZI_(G),SZJ_(G),SZCAT_(IG)), intent(in) :: h_prev, h_end
real, dimension(SZIB_(G),SZJ_(G),SZCAT_(IG)), intent(in) :: uhtr
real, dimension(SZI_(G),SZJB_(G),SZCAT_(IG)), intent(in) :: vhtr
real, intent(in) :: dt
integer, intent(in) :: ntr
type(SIS_tracer_advect_CS), pointer :: CS
!! type(ocean_OBC_type), pointer :: OBC
! This subroutine time steps the tracer concentration.
! A monotonic, conservative, weakly diffusive scheme is used.
! Arguments: h_prev - Category thickness times fractional coverage before advection, in m or kg m-2.
! (in) h_end - Layer thickness times fractional coverage after advection, in m or kg m-2.
! (in) uhtr - Accumulated volume or mass fluxes through zonal faces,
! in m3 s-1 or kg s-1.
! (in) vhtr - Accumulated volume or mass fluxes through meridional faces,
! in m3 s-1 or kg s-1.
!! (in) OBC - This open boundary condition type specifies whether, where,
!! and what open boundary conditions are used.
! (in) dt - Time increment in s.
! (in) G - The ocean's grid structure.
! (in) IG - The sea-ice-specific grid structure.
! (in) CS - The control structure returned by a previous call to
! SIS_tracer_advect_init.
! (in) TrReg - A pointer to the tracer registry.
real, dimension(SZI_(G),SZJ_(G),SZCAT_(IG)) :: &
hprev ! The cell volume at the end of the previous tracer
! change, in m3.
real, dimension(SZIB_(G),SZJ_(G),SZCAT_(IG)) :: &
uhr ! The remaining zonal thickness flux, in m3.
real, dimension(SZI_(G),SZJB_(G),SZCAT_(IG)) :: &
vhr ! The remaining meridional thickness fluxes, in m3.
real :: uh_neglect(SZIB_(G),SZJ_(G)) ! uh_neglect and vh_neglect are the
real :: vh_neglect(SZI_(G),SZJB_(G)) ! magnitude of remaining transports that
! can be simply discarded, in m3 or kg.
real :: landvolfill ! An arbitrary? nonzero cell volume, m3.
real :: Idt ! 1/dt in s-1.
real :: h_neglect
logical :: domore_u(SZJ_(G),SZCAT_(IG)) ! domore__ indicate whether there is more
logical :: domore_v(SZJB_(G),SZCAT_(IG)) ! advection to be done in the corresponding
! row or column.
logical :: x_first ! If true, advect in the x-direction first.
integer :: max_iter ! The maximum number of iterations in
! each layer.
integer :: domore_k(SZCAT_(IG))
integer :: stensil ! The stensil of the advection scheme.
integer :: nsten_halo ! The number of stensils that fit in the halos.
integer :: i, j, k, l, m, is, ie, js, je, isd, ied, jsd, jed
integer :: ncat, nL_max, itt, do_any
integer :: isv, iev, jsv, jev ! The valid range of the indices.
is = G%isc ; ie = G%iec ; js = G%jsc ; je = G%jec ; ncat = IG%CatIce
isd = G%isd ; ied = G%ied ; jsd = G%jsd ; jed = G%jed
landvolfill = 1.0e-20 ! This is arbitrary, but must be positive.
stensil = 2 ! The scheme's stensil; 2 for PLM.
if (.not. associated(CS)) call SIS_error(FATAL, "SIS_tracer_advect: "// &
"SIS_tracer_advect_init must be called before advect_tracer.")
if (ntr==0) return
x_first = (MOD(G%first_direction,2) == 0)
Idt = 1.0/dt
nL_max = 0
do m=1,ntr ; nL_max = max(Tr(m)%nL,nL_max) ; enddo
max_iter = 3
if (CS%dt > 0.0) max_iter = 2*INT(CEILING(dt/CS%dt)) + 1
! This initializes the halos of uhr and vhr because pass_vector might do
! calculations on them, even though they are never used.
uhr(:,:,:) = 0.0 ; vhr(:,:,:) = 0.0
hprev(:,:,:) = landvolfill
h_neglect = IG%H_subroundoff
! Initialize domore_u and domore_v to .false.; they will be reevaluated later.
domore_u(:,:) = .false. ; domore_v(:,:) = .false.
!$OMP parallel default(none) shared(ncat,is,ie,js,je,domore_k,uhr,vhr,uhtr,vhtr,dt, &
!$OMP hprev,G,h_prev,h_end,isd,ied,jsd,jed,uh_neglect, &
!$OMP h_neglect,vh_neglect,ntr,Tr,domore_u,domore_v)
!$OMP do
do k=1,ncat
domore_k(k)=1
! Put the remaining (total) thickness fluxes into uhr and vhr.
do j=js,je ; do I=is-1,ie ; uhr(I,j,k) = dt*uhtr(I,j,k) ; enddo ; enddo
do J=js-1,je ; do i=is,ie ; vhr(i,J,k) = dt*vhtr(i,J,k) ; enddo ; enddo
! Find the previous total mass (or volume) of ice, but in the case that this
! category is now dramatically thinner than it was previously, add a tiny
! bit of extra mass to avoid nonsensical tracer concentrations. This will
! lead rarely to a very slight non-conservation of tracers, but not mass.
do j=js,je; do i=is,ie
hprev(i,j,k) = G%areaT(i,j) * (h_prev(i,j,k) + &
max(0.0, 1.0e-13*h_prev(i,j,k) - h_end(i,j,k)))
if (h_end(i,j,k) - h_prev(i,j,k) + ((uhr(I,j,k) - uhr(I-1,j,k)) + &
(vhr(i,J,k) - vhr(i,J-1,k))) * G%IareaT(i,j) > &
1e-10*(h_end(i,j,k) + h_prev(i,j,k))) then
!$OMP critical
call SIS_error(WARNING, "Apparently inconsistent h_prev, h_end, uhr and vhr in advect_tracer.")
!$OMP end critical
endif
enddo ; enddo
enddo
!$OMP end do nowait
!$OMP do
do j=jsd,jed ; do I=isd,ied-1
uh_neglect(I,j) = h_neglect*MIN(G%areaT(i,j),G%areaT(i+1,j))
enddo ; enddo
!$OMP end do nowait
!$OMP do
do J=jsd,jed-1 ; do i=isd,ied
vh_neglect(i,J) = h_neglect*MIN(G%areaT(i,j),G%areaT(i,j+1))
enddo ; enddo
!$OMP end do nowait
!$OMP do
do m=1,ntr
if (associated(Tr(m)%ad2d_x)) then
do j=jsd,jed ; do i=isd,ied ; Tr(m)%ad2d_x(I,j) = 0.0 ; enddo ; enddo
endif
if (associated(Tr(m)%ad2d_y)) then
do J=jsd,jed ; do i=isd,ied ; Tr(m)%ad2d_y(i,J) = 0.0 ; enddo ; enddo
endif
if (associated(Tr(m)%ad3d_x)) then
do k=1,ncat ; do j=jsd,jed ; do i=isd,ied
Tr(m)%ad3d_x(I,j,k) = 0.0
enddo ; enddo ; enddo
endif
if (associated(Tr(m)%ad3d_y)) then
do k=1,ncat ; do J=jsd,jed ; do i=isd,ied
Tr(m)%ad3d_y(i,J,k) = 0.0
enddo ; enddo ; enddo
endif
if (associated(Tr(m)%ad4d_x)) then
do l=1,Tr(m)%nL ; do k=1,ncat ; do j=jsd,jed ; do i=isd,ied
Tr(m)%ad4d_x(I,j,k,l) = 0.0
enddo ; enddo ; enddo ; enddo
endif
if (associated(Tr(m)%ad4d_y)) then
do l=1,Tr(m)%nL ; do k=1,ncat ; do J=jsd,jed ; do i=isd,ied
Tr(m)%ad4d_y(i,J,k,l) = 0.0
enddo ; enddo ; enddo ; enddo
endif
enddo
!$OMP end parallel
isv = is ; iev = ie ; jsv = js ; jev = je
do itt=1,max_iter
if (isv > is-stensil) then
call cpu_clock_begin(id_clock_pass)
call pass_vector(uhr, vhr, G%Domain)
do m=1,ntr ; do l=1,Tr(m)%nL
call pass_var(Tr(m)%t(:,:,:,l), G%Domain, complete=.false.)
enddo ; enddo
call pass_var(hprev, G%Domain)
call cpu_clock_end(id_clock_pass)
nsten_halo = min(is-isd,ied-ie,js-jsd,jed-je)/stensil
isv = is-nsten_halo*stensil ; jsv = js-nsten_halo*stensil
iev = ie+nsten_halo*stensil ; jev = je+nsten_halo*stensil
! Reevaluate domore_u & domore_v unless the valid range is the same size as
! before. Also, do this if there is Strang splitting.
if ((nsten_halo > 1) .or. (itt==1)) then
!$OMP parallel do default(none) shared(ncat,domore_k,isv,iev,jsv,jev,stensil, &
!$OMP domore_u,uhr,vhr,domore_v)
do k=1,ncat ; if (domore_k(k) > 0) then
do j=jsv,jev ; if (.not.domore_u(j,k)) then
do i=isv+stensil-1,iev-stensil; if (uhr(I,j,k) /= 0.0) then
domore_u(j,k) = .true. ; exit
endif ; enddo ! i-loop
endif ; enddo
do J=jsv+stensil-1,jev-stensil ; if (.not.domore_v(J,k)) then
do i=isv+stensil,iev-stensil; if (vhr(i,J,k) /= 0.0) then
domore_v(J,k) = .true. ; exit
endif ; enddo ! i-loop
endif ; enddo
! At this point, domore_k is global. Change it so that it indicates
! whether any work is needed on a layer on this processor.
domore_k(k) = 0
do j=jsv,jev ; if (domore_u(j,k)) domore_k(k) = 1 ; enddo
do J=jsv+stensil-1,jev-stensil ; if (domore_v(J,k)) domore_k(k) = 1 ; enddo
endif ; enddo ! k-loop
endif
endif
! Set the range of valid points after this iteration.
isv = isv + stensil ; iev = iev - stensil
jsv = jsv + stensil ; jev = jev - stensil
!$OMP parallel do default(none) shared(ncat,domore_k,x_first,Tr,hprev,uhr,uh_neglect, &
!$OMP domore_u,ntr,nL_max,Idt,isv,iev,jsv,jev, &
!$OMP stensil,G,CS,vhr,vh_neglect,domore_v,IG)
do k=1,ncat ; if (domore_k(k) > 0) then
! To ensure positive definiteness of the thickness at each iteration, the
! mass fluxes out of each layer are checked each step, and limited to keep
! the thicknesses positive. This means that several iteration may be required
! for all the transport to happen. The sum over domore_k keeps the processors
! synchronized. This may not be very efficient, but it should be reliable.
if (x_first) then
! First, advect zonally.
call advect_x(Tr, hprev, uhr, uh_neglect, domore_u, ntr, nL_max, Idt, &
isv, iev, jsv-stensil, jev+stensil, k, G, IG, &
CS%usePPM, CS%usePCM) !(, OBC)
! Next, advect meridionally.
call advect_y(Tr, hprev, vhr, vh_neglect, domore_v, ntr, nL_max, Idt, &
isv, iev, jsv, jev, k, G, IG, CS%usePPM, CS%usePCM) !(, OBC)
domore_k(k) = 0
do j=jsv-stensil,jev+stensil ; if (domore_u(j,k)) domore_k(k) = 1 ; enddo
do J=jsv-1,jev ; if (domore_v(J,k)) domore_k(k) = 1 ; enddo
else
! First, advect meridionally.
call advect_y(Tr, hprev, vhr, vh_neglect, domore_v, ntr, nL_max, Idt, &
isv-stensil, iev+stensil, jsv, jev, k, G, IG, &
CS%usePPM, CS%usePCM) !(, OBC)
! Next, advect zonally.
call advect_x(Tr, hprev, uhr, uh_neglect, domore_u, ntr, nL_max, Idt, &
isv, iev, jsv, jev, k, G, IG, CS%usePPM, CS%usePCM) !(, OBC)
domore_k(k) = 0
do j=jsv,jev ; if (domore_u(j,k)) domore_k(k) = 1 ; enddo
do J=jsv-1,jev ; if (domore_v(J,k)) domore_k(k) = 1 ; enddo
endif
endif ; enddo ! End of k-loop
! If the advection just isn't finishing after max_iter, move on.
if (itt >= max_iter) exit
! Exit if there are no layers that need more iterations.
if (isv > is-stensil) then
do_any = 0
call cpu_clock_begin(id_clock_sync)
call sum_across_PEs(domore_k(:), ncat)
call cpu_clock_end(id_clock_sync)
do k=1,ncat ; do_any = do_any + domore_k(k) ; enddo
if (do_any == 0) exit
endif
enddo ! Iterations loop
end subroutine advect_tracer
subroutine advect_scalar(scalar, h_prev, h_end, uhtr, vhtr, dt, G, IG, CS) ! (, OBC)
type(SIS_hor_grid_type), intent(inout) :: G
type(ice_grid_type), intent(inout) :: IG
real, dimension(SZI_(G),SZJ_(G),SZCAT_(IG)), intent(inout) :: scalar !< Scalar field to be advected
real, dimension(SZI_(G),SZJ_(G),SZCAT_(IG)), intent(in) :: h_prev, h_end
real, dimension(SZIB_(G),SZJ_(G),SZCAT_(IG)), intent(in) :: uhtr
real, dimension(SZI_(G),SZJB_(G),SZCAT_(IG)), intent(in) :: vhtr
real, intent(in) :: dt
type(SIS_tracer_advect_CS), pointer :: CS
! Arguments: scalar - The scalar tracer field to be advected, in arbitrary units.
! (in) h_prev - Category thickness times fractional coverage before advection, in m or kg m-2.
! (in) h_end - Layer thickness times fractional coverage after advection, in m or kg m-2.
! (in) uhtr - Accumulated volume or mass fluxes through zonal faces,
! in m3 s-1 or kg s-1.
! (in) vhtr - Accumulated volume or mass fluxes through meridional faces,
! in m3 s-1 or kg s-1.
! (in) dt - Time increment in s.
! (in) G - The ocean's grid structure.
! (in) IG - The sea-ice-specific grid structure.
! (in) CS - The control structure returned by a previous call to
! SIS_tracer_advect_init.
real, dimension(SZI_(G),SZJ_(G),SZCAT_(IG)) :: &
hprev ! The cell volume at the end of the previous tracer
! change, in m3.
real, dimension(SZIB_(G),SZJ_(G),SZCAT_(IG)) :: &
uhr ! The remaining zonal thickness flux, in m3.
real, dimension(SZI_(G),SZJB_(G),SZCAT_(IG)) :: &
vhr ! The remaining meridional thickness fluxes, in m3.
real :: uh_neglect(SZIB_(G),SZJ_(G)) ! uh_neglect and vh_neglect are the
real :: vh_neglect(SZI_(G),SZJB_(G)) ! magnitude of remaining transports that
! can be simply discarded, in m3 or kg.
real :: landvolfill ! An arbitrary? nonzero cell volume, m3.
real :: Idt ! 1/dt in s-1.
real :: h_neglect
logical :: domore_u(SZJ_(G),SZCAT_(IG)) ! domore__ indicate whether there is more
logical :: domore_v(SZJB_(G),SZCAT_(IG)) ! advection to be done in the corresponding
! row or column.
logical :: x_first ! If true, advect in the x-direction first.
integer :: max_iter ! The maximum number of iterations in
! each layer.
real, dimension(SZIB_(G),SZJ_(G)) :: flux_U2d_x ! x-direction tracer fluxes, in conc * kg
real, dimension(SZI_(G),SZJB_(G)) :: flux_U2d_y ! y-direction tracer fluxes, in conc * kg
real :: tr_up ! Upwind tracer concentrations, in conc.
real :: vol_end, Ivol_end ! Cell volume at the end of a step and its inverse.
integer :: domore_k(SZCAT_(IG))
integer :: stensil ! The stensil of the advection scheme.
integer :: nsten_halo ! The number of stensils that fit in the halos.
integer :: i, j, k, l, m, is, ie, js, je, isd, ied, jsd, jed
integer :: ncat, nL_max, itt, do_any
integer :: isv, iev, jsv, jev ! The valid range of the indices.
is = G%isc ; ie = G%iec ; js = G%jsc ; je = G%jec ; ncat = IG%CatIce
isd = G%isd ; ied = G%ied ; jsd = G%jsd ; jed = G%jed
landvolfill = 1.0e-20 ! This is arbitrary, but must be positive.
stensil = 2 ! The scheme's stensil; 2 for PLM.
if (.not. associated(CS)) call SIS_error(FATAL, "advect_scalar: "// &
"SIS_tracer_advect_init must be called before advect_scalar.")
if (CS%use_upwind2d) then
!$OMP parallel do default(none) shared(is,ie,js,je,ncat,uhtr,vhtr,dt,G,h_end, &
!$OMP h_prev,scalar) &
!$OMP private(tr_up,flux_U2d_x,flux_U2d_y,vol_end,Ivol_end)
do k=1,ncat
do j=js,je ; do I=is-1,ie
if (uhtr(I,j,k) >= 0.0) then ; tr_up = scalar(i,j,k)
else ; tr_up = scalar(i+1,j,k) ; endif
flux_U2d_x(I,j) = (dt*uhtr(I,j,k)) * tr_up
enddo ; enddo
do J=js-1,je ; do i=is,ie
if (vhtr(i,J,k) >= 0.0) then ; tr_up = scalar(i,j,k)
else ; tr_up = scalar(i,j+1,k) ; endif
flux_U2d_y(i,J) = (dt*vhtr(i,J,k)) * tr_up
enddo ; enddo
do j=js,je ; do i=is,ie
vol_end = (G%areaT(i,j) * h_end(i,j,k))
Ivol_end = 0.0 ; if (vol_end > 0.0) Ivol_end = 1.0 / vol_end
scalar(i,j,k) = ( (G%areaT(i,j)*h_prev(i,j,k))*scalar(i,j,k) - &
((flux_U2d_x(I,j) - flux_U2d_x(I-1,j)) + &
(flux_U2d_y(i,J) - flux_U2d_y(i,J-1))) ) * Ivol_end
enddo ; enddo
enddo
else
x_first = (MOD(G%first_direction,2) == 0)
Idt = 1.0/dt
max_iter = 3
if (CS%dt > 0.0) max_iter = 2*INT(CEILING(dt/CS%dt)) + 1
! This initializes the halos of uhr and vhr because pass_vector might do
! calculations on them, even though they are never used.
uhr(:,:,:) = 0.0 ; vhr(:,:,:) = 0.0
hprev(:,:,:) = landvolfill
h_neglect = IG%H_subroundoff
! Initialize domore_u and domore_v. Curiously, the value used for
! initialization does not matter to the solutions, because if .false.
! they are reevaluated after the first halo update (and always on the first
! iteration, and if .true. a number of fluxes are exactly 0 anyway. Of the
! two choices, .false. is more efficient in that it avoids extra
! calculations of 0 fluxes.
domore_u(:,:) = .false. ; domore_v(:,:) = .false.
!$OMP parallel default(none) shared(is,ie,js,je,ncat,domore_k,uhr,vhr,uhtr,vhtr,dt,G, &
!$OMP hprev,h_prev,h_end,isd,ied,jsd,jed,uh_neglect, &
!$OMP h_neglect,vh_neglect,domore_u,domore_v)
!$OMP do
do k=1,ncat
domore_k(k)=1
! Put the remaining (total) thickness fluxes into uhr and vhr.
do j=js,je ; do I=is-1,ie ; uhr(I,j,k) = dt*uhtr(I,j,k) ; enddo ; enddo
do J=js-1,je ; do i=is,ie ; vhr(i,J,k) = dt*vhtr(i,J,k) ; enddo ; enddo
! Find the previous total mass (or volume) of ice, but in the case that this
! category is now dramatically thinner than it was previously, add a tiny
! bit of extra mass to avoid nonsensical tracer concentrations. This will
! lead rarely to a very slight non-conservation of tracers, but not mass.
do i=is,ie ; do j=js,je
hprev(i,j,k) = G%areaT(i,j) * (h_prev(i,j,k) + &
max(0.0, 1.0e-13*h_prev(i,j,k) - h_end(i,j,k)))
if (h_end(i,j,k) - h_prev(i,j,k) + ((uhr(I,j,k) - uhr(I-1,j,k)) + &
(vhr(i,J,k) - vhr(i,J-1,k))) * G%IareaT(i,j) > &
1e-10*(h_end(i,j,k) + h_prev(i,j,k))) then
!$OMP critical
call SIS_error(WARNING, "Apparently inconsistent h_prev, h_end, uhr and vhr in advect_tracer.")
!$OMP end critical
endif
enddo ; enddo
enddo
!$OMP end do nowait
!$OMP do
do j=jsd,jed ; do I=isd,ied-1
uh_neglect(I,j) = h_neglect*MIN(G%areaT(i,j),G%areaT(i+1,j))
enddo ; enddo
!$OMP end do nowait
!$OMP do
do J=jsd,jed-1 ; do i=isd,ied
vh_neglect(i,J) = h_neglect*MIN(G%areaT(i,j),G%areaT(i,j+1))
enddo ; enddo
!$OMP end parallel
isv = is ; iev = ie ; jsv = js ; jev = je
do itt=1,max_iter
if (isv > is-stensil) then
call cpu_clock_begin(id_clock_pass)
call pass_vector(uhr, vhr, G%Domain)
call pass_var(scalar, G%Domain, complete=.false.)
call pass_var(hprev, G%Domain)
call cpu_clock_end(id_clock_pass)
nsten_halo = min(is-isd,ied-ie,js-jsd,jed-je)/stensil
isv = is-nsten_halo*stensil ; jsv = js-nsten_halo*stensil
iev = ie+nsten_halo*stensil ; jev = je+nsten_halo*stensil
! Reevaluate domore_u & domore_v unless the valid range is the same size as
! before. Also, do this if there is Strang splitting.
if ((nsten_halo > 1) .or. (itt==1)) then
!$OMP parallel do default(none) shared(isv,iev,jsv,jev,ncat,domore_k,domore_u,domore_v, &
!$OMP stensil,uhr,vhr)
do k=1,ncat ; if (domore_k(k) > 0) then
do j=jsv,jev ; if (.not.domore_u(j,k)) then
do i=isv+stensil-1,iev-stensil; if (uhr(I,j,k) /= 0.0) then
domore_u(j,k) = .true. ; exit
endif ; enddo ! i-loop
endif ; enddo
do J=jsv+stensil-1,jev-stensil ; if (.not.domore_v(J,k)) then
do i=isv+stensil,iev-stensil; if (vhr(i,J,k) /= 0.0) then
domore_v(J,k) = .true. ; exit
endif ; enddo ! i-loop
endif ; enddo
! At this point, domore_k is global. Change it so that it indicates
! whether any work is needed on a layer on this processor.
domore_k(k) = 0
do j=jsv,jev ; if (domore_u(j,k)) domore_k(k) = 1 ; enddo
do J=jsv+stensil-1,jev-stensil ; if (domore_v(J,k)) domore_k(k) = 1 ; enddo
endif ; enddo ! k-loop
endif
endif
! Set the range of valid points after this iteration.
isv = isv + stensil ; iev = iev - stensil
jsv = jsv + stensil ; jev = jev - stensil
!$OMP parallel do default(none) shared(ncat,isv,iev,jsv,jev,x_first,domore_k,scalar, &
!$OMP hprev,uhr,uh_neglect,domore_u,Idt,stensil,G, &
!$OMP CS,vhr,vh_neglect,domore_v,IG)
do k=1,ncat ; if (domore_k(k) > 0) then
! To ensure positive definiteness of the thickness at each iteration, the
! mass fluxes out of each layer are checked each step, and limited to keep
! the thicknesses positive. This means that several iteration may be required
! for all the transport to happen. The sum over domore_k keeps the processors
! synchronized. This may not be very efficient, but it should be reliable.
if (x_first) then
! First, advect zonally.
call advect_scalar_x(scalar, hprev, uhr, uh_neglect, domore_u, Idt, &
isv, iev, jsv-stensil, jev+stensil, k, G, IG, CS%usePPM, CS%usePCM) !(, OBC)
! Next, advect meridionally.
call advect_scalar_y(scalar, hprev, vhr, vh_neglect, domore_v, Idt, &
isv, iev, jsv, jev, k, G, IG, CS%usePPM, CS%usePCM) !(, OBC)
domore_k(k) = 0
do j=jsv-stensil,jev+stensil ; if (domore_u(j,k)) domore_k(k) = 1 ; enddo
do J=jsv-1,jev ; if (domore_v(J,k)) domore_k(k) = 1 ; enddo
else
! First, advect meridionally.
call advect_scalar_y(scalar, hprev, vhr, vh_neglect, domore_v, Idt, &
isv-stensil, iev+stensil, jsv, jev, k, G, IG, CS%usePPM, CS%usePCM) !(, OBC)
! Next, advect zonally.
call advect_scalar_x(scalar, hprev, uhr, uh_neglect, domore_u, Idt, &
isv, iev, jsv, jev, k, G, IG, CS%usePPM, CS%usePCM) !(, OBC)
domore_k(k) = 0
do j=jsv,jev ; if (domore_u(j,k)) domore_k(k) = 1 ; enddo
do J=jsv-1,jev ; if (domore_v(J,k)) domore_k(k) = 1 ; enddo
endif
endif ; enddo ! End of k-loop
! If the advection just isn't finishing after max_iter, move on.
if (itt >= max_iter) exit
! Exit if there are no layers that need more iterations.
if (isv > is-stensil) then
do_any = 0
call cpu_clock_begin(id_clock_sync)
call sum_across_PEs(domore_k(:), ncat)
call cpu_clock_end(id_clock_sync)
do k=1,ncat ; do_any = do_any + domore_k(k) ; enddo
if (do_any == 0) exit
endif
enddo ! Iterations loop
endif
end subroutine advect_scalar
subroutine advect_scalar_x(scalar, hprev, uhr, uh_neglect, domore_u, Idt, &
is, ie, js, je, k, G, IG, usePPM, usePCM) ! (, OBC)
type(SIS_hor_grid_type), intent(inout) :: G
type(ice_grid_type), intent(inout) :: IG
real, dimension(SZI_(G),SZJ_(G),SZCAT_(IG)), intent(inout) :: scalar
real, dimension(SZI_(G),SZJ_(G),SZCAT_(IG)), intent(inout) :: hprev
real, dimension(SZIB_(G),SZJ_(G),SZCAT_(IG)), intent(inout) :: uhr
real, dimension(SZIB_(G),SZJ_(G)), intent(inout) :: uh_neglect
!! type(ocean_OBC_type), pointer :: OBC
logical, dimension(SZJ_(G),SZCAT_(IG)), intent(inout) :: domore_u
real, intent(in) :: Idt
integer, intent(in) :: is, ie, js, je, k
logical, intent(in) :: usePPM, usePCM
! This subroutine does 1-d flux-form advection in the zonal direction using
! a monotonic piecewise linear scheme.
real, dimension(SZI_(G)) :: &
slope_x ! The concentration slope per grid point in units of
! concentration (nondim.).
real, dimension(SZIB_(G)) :: &
Tr_x ! The tracer concentration averaged over the water flux
! across a zonal boundary in conc.
real, dimension(SZIB_(G),SZJ_(G)) :: &
mass_mask ! A multiplicative mask at velocity points that is 1 if
! both neighboring cells have any mass, and 0 otherwise.
real :: maxslope ! The maximum concentration slope per grid point consistent
! with monotonicity, in conc. (nondim.).
real :: hup, hlos ! hup is the upwind volume, hlos is the part of that volume
! that might be lost due to advection out the other side of
! the grid box, both in m3 or kg.
real, dimension(SZIB_(G)) :: &
uhh, & ! The zonal flux that occurs during the current iteration, in m3 or kg.
CFL ! A nondimensional work variable.
real, dimension(SZI_(G)) :: &
hlst, Ihnew, & ! Work variables with units of m3 or kg and m-3 or kg-1.
haddE, haddW ! Tiny amounts of thickness that should be added to the
! tracer update with concentrations that match the average
! over the fluxes through the faces to the nominal east
! and west of the present cell, in m3 or kg.
real :: hnew ! The projected thickness, in m3 or kg.
real :: h_add ! A tiny thickness to add to keep the new tracer calculation
! well defined in the limit of vanishing layers in m3 or kg.
real :: I_htot ! The inverse of the sum of thickness within or passing or
! out of a cell, in m3 or kg.
real :: h_neglect ! A thickness that is so small it is usually lost
! in roundoff and can be neglected, in m.
logical :: do_i(SZI_(G)) ! If true, work on given points.
logical :: do_any_i
integer :: i, j
! real :: aR, aL, dMx, dMn, Tp, Tc, Tm, dA, mA, a6
logical :: usePLMslope
usePLMslope = .not.(usePCM .or. usePPM)
h_neglect = IG%H_subroundoff
do I=is-1,ie ; CFL(I) = 0.0 ; enddo
if (usePCM) then ; do i=is-1,ie+1 ; slope_x(i) = 0.0 ; enddo ; endif
do j=js,je ; if (domore_u(j,k)) then
domore_u(j,k) = .false.
if (usePPM .or. usePLMslope) then ; do I=is-2,ie+1
mass_mask(I,j) = 0.0
if (G%mask2dCu(I,j) * hprev(i,j,k)*hprev(i+1,j,k) > 0.0) mass_mask(I,j) = 1.0
enddo ; endif
! Calculate the i-direction profiles (slopes) of each tracer that is being advected.
if (usePLMslope) then
call kernel_PLM_slope_x(G, is-1, ie+1, j, scalar(:,:,k), mass_mask, slope_x(:))
endif ! usePLMslope
call kernel_uhh_CFL_x(G, is-1, ie, j, hprev(:,:,k), uhr(:,:,k), uhh, CFL, &
domore_u(j,k), h_neglect)
if (usePPM) then
call kernel_PPMH3_Tr_x(G, is-1, ie, j, &
scalar(:,:,k), mass_mask, uhh, CFL, Tr_x(:))
else ! PLM
call kernel_PLM_Tr_x(G, is-1, ie, j, &
scalar(:,:,k), uhh, CFL, slope_x(:), Tr_x(:))
endif ! usePPM
! Calculate new tracer concentration in each cell after accounting for the i-direction fluxes.
! call kernel_uhr_x(G, is, ie, j, uh_neglect, uhh, uhr(:,:,k), hprev(:,:,k), hlst, Ihnew, do_i)
do I=is-1,ie
uhr(I,j,k) = uhr(I,j,k) - uhh(I)
if (abs(uhr(I,j,k)) < uh_neglect(I,j)) uhr(I,j,k) = 0.0
enddo
do i=is,ie
if ((uhh(I) /= 0.0) .or. (uhh(I-1) /= 0.0)) then
do_i(i) = .true.
hlst(i) = max(hprev(i,j,k), 0.0) ! This max is here just for safety.
hnew = hprev(i,j,k) - (uhh(I) - uhh(I-1))
haddW(i) = 0.0 ; haddE(i) = 0.0
if (hnew <= 0.0) then
hnew = 0.0 ; do_i(i) = .false.
elseif (hnew < h_neglect*G%areaT(i,j)) then
! Add a bit of thickness with tracer concentrations that are
! proportional to the mass associated with fluxes and the previous
! mass in the cell.
h_add = h_neglect*G%areaT(i,j) - hnew
I_htot = 1.0 / (hlst(i) + (abs(uhh(I)) + abs(uhh(I-1))))
hlst(i) = hlst(i) + h_add*(hlst(i)*I_htot)
haddW(i) = h_add * (abs(uhh(I-1))*I_htot)
haddE(i) = h_add * (abs(uhh(I))*I_htot)
Ihnew(i) = 1.0 / (h_neglect*G%areaT(i,j))
else
Ihnew(i) = 1.0 / hnew
endif
! Store hnew as hprev for the next iteration.
hprev(i,j,k) = hnew
else ! Nothing changes in this cell, so skip it.
do_i(i) = .false.
endif
enddo
do i=is,ie ; if ((do_i(i)) .and. (Ihnew(i) > 0.0)) then
scalar(i,j,k) = (scalar(i,j,k) * hlst(i) - &
((uhh(I)-haddE(i))*Tr_x(I) - &
(uhh(I-1)+haddW(i))*Tr_x(I-1))) * Ihnew(i)
endif ; enddo
! call kernel_tracer_div_x(G, is, ie, j, do_i, hlst, Ihnew, flux_x(:), scalar(:,:,k))
endif ; enddo ! End of j-loop.
end subroutine advect_scalar_x
subroutine advect_x(Tr, hprev, uhr, uh_neglect, domore_u, ntr, nL_max, Idt, &
is, ie, js, je, k, G, IG, usePPM, usePCM) ! (, OBC)
type(SIS_hor_grid_type), intent(inout) :: G
type(ice_grid_type), intent(inout) :: IG
type(SIS_tracer_type), dimension(ntr), intent(inout) :: Tr
real, dimension(SZI_(G),SZJ_(G),SZCAT_(IG)), intent(inout) :: hprev
real, dimension(SZIB_(G),SZJ_(G),SZCAT_(IG)), intent(inout) :: uhr
real, dimension(SZIB_(G),SZJ_(G)), intent(inout) :: uh_neglect
!! type(ocean_OBC_type), pointer :: OBC
logical, dimension(SZJ_(G),SZCAT_(IG)), intent(inout) :: domore_u
real, intent(in) :: Idt
integer, intent(in) :: ntr, nL_max, is, ie, js, je,k
logical, intent(in) :: usePPM, usePCM
! This subroutine does 1-d flux-form advection in the zonal direction using
! a monotonic piecewise linear scheme.
real, dimension(SZI_(G),nL_max,ntr) :: &
slope_x ! The concentration slope per grid point in units of
! concentration (nondim.).
real, dimension(SZIB_(G),nL_max,ntr) :: &
Tr_x ! The tracer concentration averaged over the water flux
! across a zonal boundary in conc.
real, dimension(SZIB_(G),SZJ_(G)) :: &
mass_mask ! A multiplicative mask at velocity points that is 1 if
! both neighboring cells have any mass, and 0 otherwise.
real :: maxslope ! The maximum concentration slope per grid point consistent
! with monotonicity, in conc. (nondim.).
real :: hup, hlos ! hup is the upwind volume, hlos is the part of that volume
! that might be lost due to advection out the other side of
! the grid box, both in m3 or kg.
real, dimension(SZIB_(G)) :: &
uhh, & ! The zonal flux that occurs during the current iteration, in m3 or kg.
CFL ! A nondimensional work variable.
real, dimension(SZI_(G)) :: &
hlst, Ihnew, & ! Work variables with units of m3 or kg and m-3 or kg-1.
haddE, haddW ! Tiny amounts of thickness that should be added to the
! tracer update with concentrations that match the average
! over the fluxes through the faces to the nominal east
! and west of the present cell, in m3 or kg.
real :: hnew ! The projected thickness, in m3 or kg.
real :: h_add ! A tiny thickness to add to keep the new tracer calculation
! well defined in the limit of vanishing layers in m3 or kg.
real :: I_htot ! The inverse of the sum of thickness within or passing or
! out of a cell, in m3 or kg.
real :: h_neglect ! A thickness that is so small it is usually lost
! in roundoff and can be neglected, in m.
logical :: do_i(SZI_(G)) ! If true, work on given points.
logical :: do_any_i
integer :: i, j, l, m
logical :: usePLMslope
usePLMslope = .not.(usePCM .or. usePPM)
h_neglect = IG%H_subroundoff
do I=is-1,ie ; CFL(I) = 0.0 ; enddo
if (usePCM) then ; do m=1,ntr ; do l=1,Tr(m)%nL ; do i=is-1,ie+1
slope_x(i,l,m) = 0.0
enddo ; enddo ; enddo ; endif
do j=js,je ; if (domore_u(j,k)) then
domore_u(j,k) = .false.
if (usePPM .or. usePLMslope) then ; do I=is-2,ie+1
mass_mask(I,j) = 0.0
if (G%mask2dCu(I,j)*hprev(i,j,k)*hprev(i+1,j,k) > 0.0) mass_mask(I,j) = 1.0
enddo ; endif
! Calculate the i-direction profiles (slopes) of each tracer that is being advected.
if (usePLMslope) then
do m=1,ntr ; do l=1,Tr(m)%nL
call kernel_PLM_slope_x(G, is-1, ie+1, j, Tr(m)%t(:,:,k,l), mass_mask, slope_x(:,l,m))
enddo ; enddo
endif ! usePLMslope
call kernel_uhh_CFL_x(G, is-1, ie, j, hprev(:,:,k), uhr(:,:,k), uhh, CFL, &
domore_u(j,k), h_neglect)
if (usePPM) then
do m=1,ntr ; do l=1,Tr(m)%nL
call kernel_PPMH3_Tr_x(G, is-1, ie, j, &
Tr(m)%t(:,:,k,l), mass_mask, uhh, CFL, Tr_x(:,l,m))
enddo ; enddo
else ! PLM
do m=1,ntr ; do l=1,Tr(m)%nL
call kernel_PLM_Tr_x(G, is-1, ie, j, &
Tr(m)%t(:,:,k,l), uhh, CFL, slope_x(:,l,m), Tr_x(:,l,m))
enddo ; enddo
endif ! usePPM
! Calculate new tracer concentration in each cell after accounting for the i-direction fluxes.
! call kernel_uhr_x(G, is, ie, j, uh_neglect, uhh, uhr(:,:,k), hprev(:,:,k), hlst, Ihnew, do_i)
do I=is-1,ie
uhr(I,j,k) = uhr(I,j,k) - uhh(I)
if (abs(uhr(I,j,k)) < uh_neglect(I,j)) uhr(I,j,k) = 0.0
enddo
do i=is,ie
if ((uhh(I) /= 0.0) .or. (uhh(I-1) /= 0.0)) then
do_i(i) = .true.
hlst(i) = max(hprev(i,j,k), 0.0) ! This max is here just for safety.
hnew = hprev(i,j,k) - (uhh(I) - uhh(I-1))
haddW(i) = 0.0 ; haddE(i) = 0.0
if (hnew <= 0.0) then
hnew = 0.0 ; do_i(i) = .false.
elseif (hnew < h_neglect*G%areaT(i,j)) then
! Add a bit of thickness with tracer concentrations that are
! proportional to the mass associated with fluxes and the previous
! mass in the cell.
h_add = h_neglect*G%areaT(i,j) - hnew
I_htot = 1.0 / (hlst(i) + (abs(uhh(I)) + abs(uhh(I-1))))
hlst(i) = hlst(i) + h_add*(hlst(i)*I_htot)
haddW(i) = h_add * (abs(uhh(I-1))*I_htot)
haddE(i) = h_add * (abs(uhh(I))*I_htot)
Ihnew(i) = 1.0 / (h_neglect*G%areaT(i,j))
else
Ihnew(i) = 1.0 / hnew
endif
! Store hnew as hprev for the next iteration.
hprev(i,j,k) = hnew
else ! Nothing changes in this cell, so skip it.
do_i(i) = .false.
endif
enddo
do m=1,ntr ; do l=1,Tr(m)%nL
! call kernel_tracer_div_x(G, is, ie, j, do_i, hlst, Ihnew, flux_x(:,l,m), Tr(m)%t(:,:,k,l))
do i=is,ie ; if ((do_i(i)) .and. (Ihnew(i) > 0.0)) then
Tr(m)%t(i,j,k,l) = (Tr(m)%t(i,j,k,l) * hlst(i) - &
((uhh(I)-haddE(i))*Tr_x(I,l,m) - &
(uhh(I-1)+haddW(i))*Tr_x(I-1,l,m))) * Ihnew(i)
endif ; enddo
! Diagnostics
if (associated(Tr(m)%ad4d_x)) then ; do i=is,ie ; if (do_i(i)) then
Tr(m)%ad4d_x(I,j,k,l) = Tr(m)%ad4d_x(I,j,k,l) + uhh(I)*Tr_x(I,l,m)*Idt
endif ; enddo ; endif
if (associated(Tr(m)%ad3d_x)) then ; do i=is,ie ; if (do_i(i)) then
Tr(m)%ad3d_x(I,j,k) = Tr(m)%ad3d_x(I,j,k) + uhh(I)*Tr_x(I,l,m)*Idt
endif ; enddo ; endif
if (associated(Tr(m)%ad2d_x)) then ; do i=is,ie ; if (do_i(i)) then
Tr(m)%ad2d_x(I,j) = Tr(m)%ad2d_x(I,j) + uhh(I)*Tr_x(I,l,m)*Idt
endif ; enddo ; endif
enddo ; enddo
endif ; enddo ! End of j-loop.
end subroutine advect_x
!> Calculate the mass flux and CFL such that the flux of tracer uses as much
!! the minimum of the remaining mass flux (uhr) and the half the mass
!! in the cell plus whatever part of its half of the mass flux that
!! the flux through the other side does not require.
subroutine kernel_uhh_CFL_x(G, is, ie, j, hprev, uhr, uhh, CFL, domore_u, h_neglect)
type(SIS_hor_grid_type), intent(in) :: G
integer, intent(in) :: is, ie, j
real, dimension(SZI_(G),SZJ_(G)), intent(in) :: hprev
real, dimension(SZIB_(G),SZJ_(G)), intent(in) :: uhr
real, dimension(SZIB_(G)), intent(inout) :: uhh, CFL
logical, intent(inout) :: domore_u
real, intent(in) :: h_neglect
! Local
integer :: i
real :: hup, hlos
do I=is,ie
if (uhr(I,j) == 0.0) then
uhh(I) = 0.0
CFL(I) = 0.0
elseif (uhr(I,j) < 0.0) then
hup = hprev(i+1,j)
hlos = MAX(0.0,uhr(I+1,j))
if (((hup + uhr(I,j) - hlos) < 0.0) .and. &
((0.5*hup + uhr(I,j)) < 0.0)) then
uhh(I) = MIN(-0.5*hup,-hup+hlos,0.0)
domore_u = .true.
else
uhh(I) = uhr(I,j)
endif
CFL(I) = - uhh(I)/(hprev(i+1,j)+h_neglect) ! CFL is positive
else
hup = hprev(i,j)
hlos = MAX(0.0,-uhr(I-1,j))
if (((hup - uhr(I,j) - hlos) < 0.0) .and. &
((0.5*hup - uhr(I,j)) < 0.0)) then
uhh(I) = MAX(0.5*hup,hup-hlos,0.0)
domore_u = .true.
else
uhh(I) = uhr(I,j)
endif
CFL(I) = uhh(I)/(hprev(i,j)+h_neglect) ! CFL is positive
endif
enddo
end subroutine kernel_uhh_CFL_x
subroutine kernel_PLM_slope_x(G, is, ie, j, scalar, uMask, slope_x)
type(SIS_hor_grid_type), intent(in) :: G
integer, intent(in) :: is, ie, j
real, dimension(SZI_(G),SZJ_(G)), intent(in) :: scalar
real, dimension(SZIB_(G),SZJ_(G)), intent(in) :: uMask
real, dimension(SZI_(G)), intent(inout) :: slope_x
! Local
integer :: i
real :: Tp, Tc, Tm, dMx, dMn
do i = is, ie
Tp = scalar(i+1,j) ; Tc = scalar(i,j) ; Tm = scalar(i-1,j)
dMx = max( Tp, Tc, Tm ) - Tc
dMn= Tc - min( Tp, Tc, Tm )
slope_x(i) = uMask(I,j)*uMask(I-1,j) * &
sign( min(0.5*abs(Tp-Tm), 2.0*dMx, 2.0*dMn), Tp-Tm )
enddo
end subroutine kernel_PLM_slope_x
subroutine kernel_PLM_Tr_x(G, is, ie, j, scalar, uhh, CFL, slope_x, Tr_x)
type(SIS_hor_grid_type), intent(in) :: G
integer, intent(in) :: is, ie, j
real, dimension(SZI_(G),SZJ_(G)), intent(in) :: scalar
real, dimension(SZIB_(G)), intent(in) :: uhh, CFL
real, dimension(SZI_(G)), intent(in) :: slope_x
real, dimension(SZIB_(G)), intent(inout) :: Tr_x
! Local
integer :: i
real :: Tc
do I=is,ie
if (uhh(I) >= 0.0) then
Tc = scalar(i,j)
Tr_x(I) = Tc + 0.5 * slope_x(i) * ( 1. - CFL(I) )