! !git $Id$ !svn $Id: tl_step2d.F 1151 2023-02-09 03:08:53Z arango $ !================================================== Hernan G. Arango === ! Copyright (c) 2002-2023 The ROMS/TOMS Group Andrew M. Moore ! ! Licensed under a MIT/X style license ! ! See License_ROMS.md ! !======================================================================= ! ! ! This subroutine performs a fast (predictor or corrector) time-step ! ! for the free-surface and 2D momentum tangent linear equations. ! ! It also calculates the time filtering variables over all fast-time ! ! steps to damp high frequency signals in 3D applications. ! ! ! !======================================================================= ! MODULE tl_step2d_mod ! !git $Id$ !svn $Id: tl_step2d_LF_AM3.h 1188 2023-08-03 19:26:47Z arango $ !======================================================================= ! ! ! Tangent linear model shallow-water primitive equations predictor ! ! (Leap-frog) and corrector (Adams-Moulton) time-stepping engine. ! ! ! !======================================================================= ! USE mod_param USE mod_clima USE mod_coupling USE mod_forces USE mod_grid USE mod_mixing USE mod_ncparam USE mod_ocean USE mod_scalars USE mod_sources USE mod_stepping ! USE exchange_2d_mod USE mp_exchange_mod, ONLY : mp_exchange2d USE obc_volcons_mod, ONLY : obc_flux_tile, set_DUV_bc_tile USE tl_obc_volcons_mod, ONLY : tl_obc_flux_tile, & & tl_set_DUV_bc_tile USE tl_u2dbc_mod, ONLY : tl_u2dbc_tile USE tl_v2dbc_mod, ONLY : tl_v2dbc_tile USE tl_zetabc_mod, ONLY : tl_zetabc_tile ! implicit none ! PRIVATE PUBLIC :: tl_step2d ! CONTAINS ! !*********************************************************************** SUBROUTINE tl_step2d (ng, tile) !*********************************************************************** ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile ! ! Local variable declarations. ! character (len=*), parameter :: MyFile = & & "ROMS/Tangent/tl_step2d_LF_AM3.h" ! integer :: IminS, ImaxS, JminS, JmaxS integer :: LBi, UBi, LBj, UBj, LBij, UBij ! ! Set horizontal starting and ending indices for automatic private ! storage arrays. ! IminS=BOUNDS(ng)%Istr(tile)-3 ImaxS=BOUNDS(ng)%Iend(tile)+3 JminS=BOUNDS(ng)%Jstr(tile)-3 JmaxS=BOUNDS(ng)%Jend(tile)+3 ! ! Determine array lower and upper bounds in the I- and J-directions. ! LBi=BOUNDS(ng)%LBi(tile) UBi=BOUNDS(ng)%UBi(tile) LBj=BOUNDS(ng)%LBj(tile) UBj=BOUNDS(ng)%UBj(tile) ! ! Set array lower and upper bounds for MIN(I,J) directions and ! MAX(I,J) directions. ! LBij=BOUNDS(ng)%LBij UBij=BOUNDS(ng)%UBij ! CALL wclock_on (ng, iTLM, 9, 73, MyFile) CALL tl_step2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, N(ng), & & IminS, ImaxS, JminS, JmaxS, & & krhs(ng), kstp(ng), knew(ng), & & nstp(ng), nnew(ng), & & GRID(ng) % pmask, GRID(ng) % rmask, & & GRID(ng) % umask, GRID(ng) % vmask, & & GRID(ng) % fomn, & & GRID(ng) % h, GRID(ng) % tl_h, & & GRID(ng) % om_u, GRID(ng) % om_v, & & GRID(ng) % on_u, GRID(ng) % on_v, & & GRID(ng) % omn, & & GRID(ng) % pm, GRID(ng) % pn, & & GRID(ng) % dndx, GRID(ng) % dmde, & & GRID(ng) % pmon_r, GRID(ng) % pnom_r, & & GRID(ng) % pmon_p, GRID(ng) % pnom_p, & & GRID(ng) % om_r, GRID(ng) % on_r, & & GRID(ng) % om_p, GRID(ng) % on_p, & & MIXING(ng) % visc2_p, & & MIXING(ng) % visc2_r, & & COUPLING(ng) % tl_DU_avg1, & & COUPLING(ng) % tl_DU_avg2, & & COUPLING(ng) % tl_DV_avg1, & & COUPLING(ng) % tl_DV_avg2, & & COUPLING(ng) % Zt_avg1, & & COUPLING(ng) % tl_Zt_avg1, & & COUPLING(ng) % tl_rufrc, & & COUPLING(ng) % tl_rvfrc, & & OCEAN(ng) % tl_ru, & & OCEAN(ng) % tl_rv, & & OCEAN(ng) % rubar, OCEAN(ng) % tl_rubar, & & OCEAN(ng) % rvbar, OCEAN(ng) % tl_rvbar, & & OCEAN(ng) % rzeta, OCEAN(ng) % tl_rzeta, & & OCEAN(ng) % ubar, OCEAN(ng) % tl_ubar, & & OCEAN(ng) % vbar, OCEAN(ng) % tl_vbar, & & OCEAN(ng) % zeta, OCEAN(ng) % tl_zeta) CALL wclock_off (ng, iTLM, 9, 174, MyFile) ! RETURN END SUBROUTINE tl_step2d ! !*********************************************************************** SUBROUTINE tl_step2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, UBk, & & IminS, ImaxS, JminS, JmaxS, & & krhs, kstp, knew, & & nstp, nnew, & & pmask, rmask, umask, vmask, & & fomn, & & h, tl_h, & & om_u, om_v, on_u, on_v, omn, pm, pn, & & dndx, dmde, & & pmon_r, pnom_r, pmon_p, pnom_p, & & om_r, on_r, om_p, on_p, & & visc2_p, visc2_r, & & tl_DU_avg1, tl_DU_avg2, & & tl_DV_avg1, tl_DV_avg2, & & Zt_avg1, tl_Zt_avg1, & & tl_rufrc, tl_rvfrc, & & tl_ru, tl_rv, & & rubar, tl_rubar, & & rvbar, tl_rvbar, & & rzeta, tl_rzeta, & & ubar, tl_ubar, & & vbar, tl_vbar, & & zeta, tl_zeta) !*********************************************************************** ! ! Imported variable declarations. ! integer, intent(in ) :: ng, tile integer, intent(in ) :: LBi, UBi, LBj, UBj, UBk integer, intent(in ) :: IminS, ImaxS, JminS, JmaxS integer, intent(in ) :: krhs, kstp, knew integer, intent(in ) :: nstp, nnew ! real(r8), intent(in ) :: pmask(LBi:,LBj:) real(r8), intent(in ) :: rmask(LBi:,LBj:) real(r8), intent(in ) :: umask(LBi:,LBj:) real(r8), intent(in ) :: vmask(LBi:,LBj:) real(r8), intent(in ) :: fomn(LBi:,LBj:) real(r8), intent(in ) :: h(LBi:,LBj:) real(r8), intent(in ) :: om_u(LBi:,LBj:) real(r8), intent(in ) :: om_v(LBi:,LBj:) real(r8), intent(in ) :: on_u(LBi:,LBj:) real(r8), intent(in ) :: on_v(LBi:,LBj:) real(r8), intent(in ) :: omn(LBi:,LBj:) real(r8), intent(in ) :: pm(LBi:,LBj:) real(r8), intent(in ) :: pn(LBi:,LBj:) real(r8), intent(in ) :: dndx(LBi:,LBj:) real(r8), intent(in ) :: dmde(LBi:,LBj:) real(r8), intent(in ) :: pmon_r(LBi:,LBj:) real(r8), intent(in ) :: pnom_r(LBi:,LBj:) real(r8), intent(in ) :: pmon_p(LBi:,LBj:) real(r8), intent(in ) :: pnom_p(LBi:,LBj:) real(r8), intent(in ) :: om_r(LBi:,LBj:) real(r8), intent(in ) :: on_r(LBi:,LBj:) real(r8), intent(in ) :: om_p(LBi:,LBj:) real(r8), intent(in ) :: on_p(LBi:,LBj:) real(r8), intent(in ) :: visc2_p(LBi:,LBj:) real(r8), intent(in ) :: visc2_r(LBi:,LBj:) real(r8), intent(in ) :: rubar(LBi:,LBj:,:) real(r8), intent(in ) :: rvbar(LBi:,LBj:,:) real(r8), intent(in ) :: rzeta(LBi:,LBj:,:) real(r8), intent(in ) :: ubar(LBi:,LBj:,:) real(r8), intent(in ) :: vbar(LBi:,LBj:,:) real(r8), intent(in ) :: zeta(LBi:,LBj:,:) real(r8), intent(in ) :: tl_h(LBi:,LBj:) real(r8), intent(in ) :: Zt_avg1(LBi:,LBj:) real(r8), intent(inout) :: tl_DU_avg1(LBi:,LBj:) real(r8), intent(inout) :: tl_DU_avg2(LBi:,LBj:) real(r8), intent(inout) :: tl_DV_avg1(LBi:,LBj:) real(r8), intent(inout) :: tl_DV_avg2(LBi:,LBj:) real(r8), intent(inout) :: tl_Zt_avg1(LBi:,LBj:) real(r8), intent(inout) :: tl_rufrc(LBi:,LBj:) real(r8), intent(inout) :: tl_rvfrc(LBi:,LBj:) real(r8), intent(inout) :: tl_ru(LBi:,LBj:,0:,:) real(r8), intent(inout) :: tl_rv(LBi:,LBj:,0:,:) real(r8), intent(inout) :: tl_rubar(LBi:,LBj:,:) real(r8), intent(inout) :: tl_rvbar(LBi:,LBj:,:) real(r8), intent(inout) :: tl_rzeta(LBi:,LBj:,:) real(r8), intent(inout) :: tl_ubar(LBi:,LBj:,:) real(r8), intent(inout) :: tl_vbar(LBi:,LBj:,:) real(r8), intent(inout) :: tl_zeta(LBi:,LBj:,:) ! ! Local variable declarations. ! logical :: CORRECTOR_2D_STEP ! integer :: i, is, j, ptsk ! real(r8) :: cff, cff1, cff2, cff3, cff4, cff5, cff6, cff7 real(r8) :: fac, fac1, fac2, fac3 real(r8) :: tl_cff, tl_cff1, tl_cff2, tl_cff3, tl_cff4 real(r8) :: tl_fac, tl_fac1 ! real(r8), parameter :: IniVal = 0.0_r8 ! real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Dgrad real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Dnew real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Drhs real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Drhs_p real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: Dstp real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: DUon real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: DVom real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: UFe real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: UFx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: VFe real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: VFx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: grad real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: gzeta real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: gzeta2 real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: rhs_ubar real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: rhs_vbar real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: rhs_zeta real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: zeta_new real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: zwrk real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_Dgrad real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_Dnew real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_Drhs real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_Drhs_p real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_Dstp real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_DUon real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_DVom real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_UFe real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_UFx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_VFe real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_VFx real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_grad real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_gzeta real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_gzeta2 real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_rhs_ubar real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_rhs_vbar real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_rhs_zeta real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_zeta_new real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: tl_zwrk ! !----------------------------------------------------------------------- ! Set lower and upper tile bounds and staggered variables bounds for ! this horizontal domain partition. Notice that if tile=-1, it will ! set the values for the global grid. !----------------------------------------------------------------------- ! integer :: Istr, IstrB, IstrP, IstrR, IstrT, IstrM, IstrU integer :: Iend, IendB, IendP, IendR, IendT integer :: Jstr, JstrB, JstrP, JstrR, JstrT, JstrM, JstrV integer :: Jend, JendB, JendP, JendR, JendT integer :: Istrm3, Istrm2, Istrm1, IstrUm2, IstrUm1 integer :: Iendp1, Iendp2, Iendp2i, Iendp3 integer :: Jstrm3, Jstrm2, Jstrm1, JstrVm2, JstrVm1 integer :: Jendp1, Jendp2, Jendp2i, Jendp3 ! Istr =BOUNDS(ng) % Istr (tile) IstrB =BOUNDS(ng) % IstrB (tile) IstrM =BOUNDS(ng) % IstrM (tile) IstrP =BOUNDS(ng) % IstrP (tile) IstrR =BOUNDS(ng) % IstrR (tile) IstrT =BOUNDS(ng) % IstrT (tile) IstrU =BOUNDS(ng) % IstrU (tile) Iend =BOUNDS(ng) % Iend (tile) IendB =BOUNDS(ng) % IendB (tile) IendP =BOUNDS(ng) % IendP (tile) IendR =BOUNDS(ng) % IendR (tile) IendT =BOUNDS(ng) % IendT (tile) Jstr =BOUNDS(ng) % Jstr (tile) JstrB =BOUNDS(ng) % JstrB (tile) JstrM =BOUNDS(ng) % JstrM (tile) JstrP =BOUNDS(ng) % JstrP (tile) JstrR =BOUNDS(ng) % JstrR (tile) JstrT =BOUNDS(ng) % JstrT (tile) JstrV =BOUNDS(ng) % JstrV (tile) Jend =BOUNDS(ng) % Jend (tile) JendB =BOUNDS(ng) % JendB (tile) JendP =BOUNDS(ng) % JendP (tile) JendR =BOUNDS(ng) % JendR (tile) JendT =BOUNDS(ng) % JendT (tile) ! Istrm3 =BOUNDS(ng) % Istrm3 (tile) ! Istr-3 Istrm2 =BOUNDS(ng) % Istrm2 (tile) ! Istr-2 Istrm1 =BOUNDS(ng) % Istrm1 (tile) ! Istr-1 IstrUm2=BOUNDS(ng) % IstrUm2(tile) ! IstrU-2 IstrUm1=BOUNDS(ng) % IstrUm1(tile) ! IstrU-1 Iendp1 =BOUNDS(ng) % Iendp1 (tile) ! Iend+1 Iendp2 =BOUNDS(ng) % Iendp2 (tile) ! Iend+2 Iendp2i=BOUNDS(ng) % Iendp2i(tile) ! Iend+2 interior Iendp3 =BOUNDS(ng) % Iendp3 (tile) ! Iend+3 Jstrm3 =BOUNDS(ng) % Jstrm3 (tile) ! Jstr-3 Jstrm2 =BOUNDS(ng) % Jstrm2 (tile) ! Jstr-2 Jstrm1 =BOUNDS(ng) % Jstrm1 (tile) ! Jstr-1 JstrVm2=BOUNDS(ng) % JstrVm2(tile) ! JstrV-2 JstrVm1=BOUNDS(ng) % JstrVm1(tile) ! JstrV-1 Jendp1 =BOUNDS(ng) % Jendp1 (tile) ! Jend+1 Jendp2 =BOUNDS(ng) % Jendp2 (tile) ! Jend+2 Jendp2i=BOUNDS(ng) % Jendp2i(tile) ! Jend+2 interior Jendp3 =BOUNDS(ng) % Jendp3 (tile) ! Jend+3 ! ptsk=3-kstp CORRECTOR_2D_STEP=.not.PREDICTOR_2D_STEP(ng) ! !----------------------------------------------------------------------- ! Compute total depth (m) and vertically integrated mass fluxes. !----------------------------------------------------------------------- ! ! In distributed-memory, the I- and J-ranges are different and a ! special exchange is done to avoid having three ghost points for ! high order numerical stencils. Notice that a private array is ! passed below to the exchange routine. It also applies periodic ! boundary conditions, if appropriate and no partitions in I- or ! J-directions. ! DO j=JstrV-2,Jendp2 DO i=IstrU-2,Iendp2 Dnew(i,j)=zeta(i,j,knew)+h(i,j) Drhs(i,j)=zeta(i,j,krhs)+h(i,j) tl_Drhs(i,j)=tl_zeta(i,j,krhs)+tl_h(i,j) END DO END DO DO j=JstrV-2,Jendp2 DO i=IstrU-1,Iendp2 cff=0.5_r8*on_u(i,j) cff1=cff*(Drhs(i,j)+Drhs(i-1,j)) tl_cff1=cff*(tl_Drhs(i,j)+tl_Drhs(i-1,j)) DUon(i,j)=ubar(i,j,krhs)*cff1 tl_DUon(i,j)=tl_ubar(i,j,krhs)*cff1+ & & ubar(i,j,krhs)*tl_cff1 END DO END DO DO j=JstrV-1,Jendp2 DO i=IstrU-2,Iendp2 cff=0.5_r8*om_v(i,j) cff1=cff*(Drhs(i,j)+Drhs(i,j-1)) tl_cff1=cff*(tl_Drhs(i,j)+tl_Drhs(i,j-1)) DVom(i,j)=vbar(i,j,krhs)*cff1 tl_DVom(i,j)=tl_vbar(i,j,krhs)*cff1+ & & vbar(i,j,krhs)*tl_cff1 END DO END DO ! IF (EWperiodic(ng).or.NSperiodic(ng)) THEN CALL exchange_u2d_tile (ng, tile, & & IminS, ImaxS, JminS, JmaxS, & & DUon) CALL exchange_u2d_tile (ng, tile, & & IminS, ImaxS, JminS, JmaxS, & & tl_DUon) CALL exchange_v2d_tile (ng, tile, & & IminS, ImaxS, JminS, JmaxS, & & DVom) CALL exchange_v2d_tile (ng, tile, & & IminS, ImaxS, JminS, JmaxS, & & tl_DVom) END IF CALL mp_exchange2d (ng, tile, iTLM, 2, & & IminS, ImaxS, JminS, JmaxS, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & DUon, DVom) CALL mp_exchange2d (ng, tile, iTLM, 2, & & IminS, ImaxS, JminS, JmaxS, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & tl_DUon, tl_DVom) ! ! Initialize right-hand-side terms. ! DO j=Jstr,Jend DO i=Istr,Iend rhs_ubar(i,j)=0.0_r8 rhs_vbar(i,j)=0.0_r8 END DO END DO ! ! Compute integral mass flux across open boundaries and adjust ! for volume conservation. Compute BASIC STATE value. ! This needs to be computed here instead of below. ! IF (ANY(tl_VolCons(:,ng))) THEN CALL obc_flux_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & knew, & & umask, vmask, & & h, om_v, on_u, & & ubar, vbar, zeta) ! ! Set vertically integrated mass fluxes DUon and DVom along the open ! boundaries in such a way that the integral volume is conserved. ! CALL set_DUV_bc_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & krhs, & & umask, vmask, & & om_v, on_u, & & ubar, vbar, & & Drhs, DUon, DVom) CALL tl_set_DUV_bc_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & krhs, & & umask, vmask, & & om_v, on_u, ubar, vbar, & & tl_ubar, tl_vbar, & & Drhs, DUon, DVom, & & tl_Drhs, tl_DUon, tl_DVom) END IF ! !----------------------------------------------------------------------- ! Compute time averaged fields over all short time-steps. !----------------------------------------------------------------------- ! IF (PREDICTOR_2D_STEP(ng)) THEN IF (iif(ng).eq.1) THEN ! ! Reset arrays for 2D fields averaged within the short time-steps. ! cff2=(-1.0_r8/12.0_r8)*weight(2,iif(ng)+1,ng) DO j=JstrR,JendR DO i=IstrR,IendR !^ Zt_avg1(i,j)=0.0_r8 !^ tl_Zt_avg1(i,j)=0.0_r8 END DO DO i=Istr,IendR !^ DU_avg1(i,j)=0.0_r8 !^ tl_DU_avg1(i,j)=0.0_r8 !^ DU_avg2(i,j)=cff2*DUon(i,j) !^ tl_DU_avg2(i,j)=cff2*tl_DUon(i,j) END DO END DO DO j=Jstr,JendR DO i=IstrR,IendR !^ DV_avg1(i,j)=0.0_r8 !^ tl_DV_avg1(i,j)=0.0_r8 !^ DV_avg2(i,j)=cff2*DVom(i,j) !^ tl_DV_avg2(i,j)=cff2*tl_DVom(i,j) END DO END DO ELSE ! ! Accumulate field averages of previous time-step after they are ! computed in the previous corrector step, updated their boundaries, ! and synchronized. ! cff1=weight(1,iif(ng)-1,ng) cff2=(8.0_r8/12.0_r8)*weight(2,iif(ng) ,ng)- & & (1.0_r8/12.0_r8)*weight(2,iif(ng)+1,ng) DO j=JstrR,JendR DO i=IstrR,IendR !^ Zt_avg1(i,j)=Zt_avg1(i,j)+cff1*zeta(i,j,krhs) !^ tl_Zt_avg1(i,j)=tl_Zt_avg1(i,j)+cff1*tl_zeta(i,j,krhs) END DO DO i=Istr,IendR !^ DU_avg1(i,j)=DU_avg1(i,j)+cff1*DUon(i,j) !^ tl_DU_avg1(i,j)=tl_DU_avg1(i,j)+cff1*tl_DUon(i,j) !^ DU_avg2(i,j)=DU_avg2(i,j)+cff2*DUon(i,j) !^ tl_DU_avg2(i,j)=tl_DU_avg2(i,j)+cff2*tl_DUon(i,j) END DO END DO DO j=Jstr,JendR DO i=IstrR,IendR !^ DV_avg1(i,j)=DV_avg1(i,j)+cff1*DVom(i,j) !^ tl_DV_avg1(i,j)=tl_DV_avg1(i,j)+cff1*tl_DVom(i,j) !^ DV_avg2(i,j)=DV_avg2(i,j)+cff2*DVom(i,j) !^ tl_DV_avg2(i,j)=tl_DV_avg2(i,j)+cff2*tl_DVom(i,j) END DO END DO END IF ELSE IF (iif(ng).eq.1) THEN cff2=weight(2,iif(ng),ng) ELSE cff2=(5.0_r8/12.0_r8)*weight(2,iif(ng),ng) END IF DO j=JstrR,JendR DO i=Istr,IendR !^ DU_avg2(i,j)=DU_avg2(i,j)+cff2*DUon(i,j) !^ tl_DU_avg2(i,j)=tl_DU_avg2(i,j)+cff2*tl_DUon(i,j) END DO END DO DO j=Jstr,JendR DO i=IstrR,IendR !^ DV_avg2(i,j)=DV_avg2(i,j)+cff2*DVom(i,j) !^ tl_DV_avg2(i,j)=tl_DV_avg2(i,j)+cff2*tl_DVom(i,j) END DO END DO END IF ! ! After all fast time steps are completed, apply boundary conditions ! to time averaged fields. ! IF ((iif(ng).eq.(nfast(ng)+1)).and.PREDICTOR_2D_STEP(ng)) THEN IF (EWperiodic(ng).or.NSperiodic(ng)) THEN !^ CALL exchange_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & Zt_avg1) !^ CALL exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & tl_Zt_avg1) !^ CALL exchange_u2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & DU_avg1) !^ CALL exchange_u2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & tl_DU_avg1) !^ CALL exchange_v2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & DV_avg1) !^ CALL exchange_v2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & tl_DV_avg1) END IF !^ CALL mp_exchange2d (ng, tile, iNLM, 3, & !^ & LBi, UBi, LBj, UBj, & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & Zt_avg1, DU_avg1, DV_avg1) !^ CALL mp_exchange2d (ng, tile, iTLM, 3, & & LBi, UBi, LBj, UBj, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & tl_Zt_avg1, tl_DU_avg1, tl_DV_avg1) END IF ! ! Do not perform the actual time stepping during the auxiliary ! (nfast(ng)+1) time step. ! IF (iif(ng).gt.nfast(ng)) RETURN ! !======================================================================= ! Time step free-surface equation. !======================================================================= ! ! During the first time-step, the predictor step is Forward-Euler ! and the corrector step is Backward-Euler. Otherwise, the predictor ! step is Leap-frog and the corrector step is Adams-Moulton. ! IF (iif(ng).eq.1) THEN cff1=dtfast(ng) DO j=JstrV-1,Jend DO i=IstrU-1,Iend !^ rhs_zeta(i,j)=(DUon(i,j)-DUon(i+1,j))+ & !^ & (DVom(i,j)-DVom(i,j+1)) !^ tl_rhs_zeta(i,j)=(tl_DUon(i,j)-tl_DUon(i+1,j))+ & & (tl_DVom(i,j)-tl_DVom(i,j+1)) !^ zeta_new(i,j)=zeta(i,j,kstp)+ & !^ & pm(i,j)*pn(i,j)*cff1*rhs_zeta(i,j) !^ !^ use background instead zeta_new(i,j)=zeta(i,j,knew) tl_zeta_new(i,j)=tl_zeta(i,j,kstp)+ & & pm(i,j)*pn(i,j)*cff1*tl_rhs_zeta(i,j) zeta_new(i,j)=zeta_new(i,j)*rmask(i,j) tl_zeta_new(i,j)=tl_zeta_new(i,j)*rmask(i,j) !^ Dnew(i,j)=zeta_new(i,j)+h(i,j) !^ tl_Dnew(i,j)=tl_zeta_new(i,j)+tl_h(i,j) ! zwrk(i,j)=0.5_r8*(zeta(i,j,kstp)+zeta_new(i,j)) tl_zwrk(i,j)=0.5_r8*(tl_zeta(i,j,kstp)+tl_zeta_new(i,j)) gzeta(i,j)=zwrk(i,j) tl_gzeta(i,j)=tl_zwrk(i,j) gzeta2(i,j)=zwrk(i,j)*zwrk(i,j) tl_gzeta2(i,j)=2.0_r8*tl_zwrk(i,j)*zwrk(i,j) END DO END DO ELSE IF (PREDICTOR_2D_STEP(ng)) THEN cff1=2.0_r8*dtfast(ng) cff4=4.0_r8/25.0_r8 cff5=1.0_r8-2.0_r8*cff4 DO j=JstrV-1,Jend DO i=IstrU-1,Iend !^ rhs_zeta(i,j)=(DUon(i,j)-DUon(i+1,j))+ & !^ & (DVom(i,j)-DVom(i,j+1)) !^ tl_rhs_zeta(i,j)=(tl_DUon(i,j)-tl_DUon(i+1,j))+ & & (tl_DVom(i,j)-tl_DVom(i,j+1)) !^ zeta_new(i,j)=zeta(i,j,kstp)+ & !^ & pm(i,j)*pn(i,j)*cff1*rhs_zeta(i,j) !^ !^ use background instead zeta_new(i,j)=zeta(i,j,knew) tl_zeta_new(i,j)=tl_zeta(i,j,kstp)+ & & pm(i,j)*pn(i,j)*cff1*tl_rhs_zeta(i,j) zeta_new(i,j)=zeta_new(i,j)*rmask(i,j) tl_zeta_new(i,j)=tl_zeta_new(i,j)*rmask(i,j) !^ Dnew(i,j)=zeta_new(i,j)+h(i,j) !^ tl_Dnew(i,j)=tl_zeta_new(i,j)+tl_h(i,j) ! zwrk(i,j)=cff5*zeta(i,j,krhs)+ & & cff4*(zeta(i,j,kstp)+zeta_new(i,j)) tl_zwrk(i,j)=cff5*tl_zeta(i,j,krhs)+ & & cff4*(tl_zeta(i,j,kstp)+tl_zeta_new(i,j)) gzeta(i,j)=zwrk(i,j) tl_gzeta(i,j)=tl_zwrk(i,j) gzeta2(i,j)=zwrk(i,j)*zwrk(i,j) tl_gzeta2(i,j)=2.0_r8*tl_zwrk(i,j)*zwrk(i,j) END DO END DO ELSE IF (CORRECTOR_2D_STEP) THEN cff1=dtfast(ng)*5.0_r8/12.0_r8 cff2=dtfast(ng)*8.0_r8/12.0_r8 cff3=dtfast(ng)*1.0_r8/12.0_r8 cff4=2.0_r8/5.0_r8 cff5=1.0_r8-cff4 DO j=JstrV-1,Jend DO i=IstrU-1,Iend !^ cff=cff1*((DUon(i,j)-DUon(i+1,j))+ & !^ & (DVom(i,j)-DVom(i,j+1))) !^ tl_cff=cff1*((tl_DUon(i,j)-tl_DUon(i+1,j))+ & & (tl_DVom(i,j)-tl_DVom(i,j+1))) !^ zeta_new(i,j)=zeta(i,j,kstp)+ & !^ & pm(i,j)*pn(i,j)*(cff+ & !^ & cff2*rzeta(i,j,kstp)- & !^ & cff3*rzeta(i,j,ptsk)) !^ !^ use background instead zeta_new(i,j)=zeta(i,j,knew) tl_zeta_new(i,j)=tl_zeta(i,j,kstp)+ & & pm(i,j)*pn(i,j)*(tl_cff+ & & cff2*tl_rzeta(i,j,kstp)- & & cff3*tl_rzeta(i,j,ptsk)) zeta_new(i,j)=zeta_new(i,j)*rmask(i,j) tl_zeta_new(i,j)=tl_zeta_new(i,j)*rmask(i,j) !^ Dnew(i,j)=zeta_new(i,j)+h(i,j) !^ tl_Dnew(i,j)=tl_zeta_new(i,j)+tl_h(i,j) ! zwrk(i,j)=cff5*zeta_new(i,j)+cff4*zeta(i,j,krhs) tl_zwrk(i,j)=cff5*tl_zeta_new(i,j)+cff4*tl_zeta(i,j,krhs) gzeta(i,j)=zwrk(i,j) tl_gzeta(i,j)=tl_zwrk(i,j) gzeta2(i,j)=zwrk(i,j)*zwrk(i,j) tl_gzeta2(i,j)=2.0_r8*tl_zwrk(i,j)*zwrk(i,j) END DO END DO END IF ! ! Load new free-surface values into shared array at both predictor ! and corrector steps. ! DO j=Jstr,Jend DO i=Istr,Iend !^ zeta(i,j,knew)=zeta_new(i,j) !^ tl_zeta(i,j,knew)=tl_zeta_new(i,j) END DO END DO ! ! If predictor step, load right-side-term into shared array. ! IF (PREDICTOR_2D_STEP(ng)) THEN DO j=Jstr,Jend DO i=Istr,Iend !^ rzeta(i,j,krhs)=rhs_zeta(i,j) !^ tl_rzeta(i,j,krhs)=tl_rhs_zeta(i,j) END DO END DO IF (EWperiodic(ng).or.NSperiodic(ng)) THEN !^ CALL exchange_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & rzeta(:,:,krhs)) !^ CALL exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & tl_rzeta(:,:,krhs)) END IF !^ CALL mp_exchange2d (ng, tile, iNLM, 1, & !^ & LBi, UBi, LBj, UBj, & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & rzeta(:,:,krhs)) !^ CALL mp_exchange2d (ng, tile, iTLM, 1, & & LBi, UBi, LBj, UBj, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & tl_rzeta(:,:,krhs)) END IF ! ! Apply mass point sources (volume vertical influx), if any. ! ! Dsrc(is) = 2, flow across grid cell w-face (positive or negative) ! IF (LwSrc(ng)) THEN DO is=1,Nsrc(ng) IF (INT(SOURCES(ng)%Dsrc(is)).eq.2) THEN i=SOURCES(ng)%Isrc(is) j=SOURCES(ng)%Jsrc(is) IF (((IstrR.le.i).and.(i.le.IendR)).and. & & ((JstrR.le.j).and.(j.le.JendR))) THEN !^ zeta(i,j,knew)=zeta(i,j,knew)+ & !^ & SOURCES(ng)%Qbar(is)* & !^ & pm(i,j)*pn(i,j)*dtfast(ng) !^ END IF END IF END DO END IF ! ! Set free-surface lateral boundary conditions. ! !^ CALL zetabc_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & krhs, kstp, knew, & !^ & zeta) !^ CALL tl_zetabc_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & krhs, kstp, knew, & & zeta, tl_zeta) IF (EWperiodic(ng).or.NSperiodic(ng)) THEN !^ CALL exchange_r2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & zeta(:,:,knew)) !^ CALL exchange_r2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & tl_zeta(:,:,knew)) END IF !^ CALL mp_exchange2d (ng, tile, iNLM, 1, & !^ & LBi, UBi, LBj, UBj, & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & zeta(:,:,knew)) !^ CALL mp_exchange2d (ng, tile, iTLM, 1, & & LBi, UBi, LBj, UBj, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & tl_zeta(:,:,knew)) ! !======================================================================= ! Compute right-hand-side for the 2D momentum equations. !======================================================================= ! !----------------------------------------------------------------------- ! Compute pressure gradient terms. !----------------------------------------------------------------------- ! cff1=0.5_r8*g cff2=1.0_r8/3.0_r8 DO j=Jstr,Jend DO i=IstrU,Iend !^ rhs_ubar(i,j)=cff1*on_u(i,j)* & !^ & ((h(i-1,j)+ & !^ & h(i ,j))* & !^ & (gzeta(i-1,j)- & !^ & gzeta(i ,j))+ & !^ & (gzeta2(i-1,j)- & !^ & gzeta2(i ,j))) !^ tl_rhs_ubar(i,j)=cff1*on_u(i,j)* & & ((tl_h(i-1,j)+ & & tl_h(i ,j))* & & (gzeta(i-1,j)- & & gzeta(i ,j))+ & & (h(i-1,j)+ & & h(i ,j))* & & (tl_gzeta(i-1,j)- & & tl_gzeta(i ,j))+ & & (tl_gzeta2(i-1,j)- & & tl_gzeta2(i ,j))) END DO IF (j.ge.JstrV) THEN DO i=Istr,Iend !^ rhs_vbar(i,j)=cff1*om_v(i,j)* & !^ & ((h(i,j-1)+ & !^ & h(i,j ))* & !^ & (gzeta(i,j-1)- & !^ & gzeta(i,j ))+ & !^ & (gzeta2(i,j-1)- & !^ & gzeta2(i,j ))) !^ tl_rhs_vbar(i,j)=cff1*om_v(i,j)* & & ((tl_h(i,j-1)+ & & tl_h(i,j ))* & & (gzeta(i,j-1)- & & gzeta(i,j ))+ & & (h(i,j-1)+ & & h(i,j ))* & & (tl_gzeta(i,j-1)- & & tl_gzeta(i,j ))+ & & (tl_gzeta2(i,j-1)- & & tl_gzeta2(i,j ))) END DO END IF END DO ! !----------------------------------------------------------------------- ! Add in horizontal advection of momentum. !----------------------------------------------------------------------- ! ! Fourth-order, centered differences advection. ! DO j=Jstr,Jend DO i=IstrUm1,Iendp1 grad (i,j)=ubar(i-1,j,krhs)-2.0_r8*ubar(i,j,krhs)+ & & ubar(i+1,j,krhs) tl_grad(i,j)=tl_ubar(i-1,j,krhs)-2.0_r8*tl_ubar(i,j,krhs)+ & & tl_ubar(i+1,j,krhs) Dgrad(i,j)=DUon(i-1,j)-2.0_r8*DUon(i,j)+DUon(i+1,j) tl_Dgrad(i,j)=tl_DUon(i-1,j)-2.0_r8*tl_DUon(i,j)+ & & tl_DUon(i+1,j) END DO END DO IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN DO j=Jstr,Jend grad (Istr,j)=grad (Istr+1,j) tl_grad (Istr,j)=tl_grad (Istr+1,j) Dgrad(Istr,j)=Dgrad(Istr+1,j) tl_Dgrad(Istr,j)=tl_Dgrad(Istr+1,j) END DO END IF END IF IF (.not.(CompositeGrid(ieast,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN DO j=Jstr,Jend grad (Iend+1,j)=grad (Iend,j) tl_grad (Iend+1,j)=tl_grad (Iend,j) Dgrad(Iend+1,j)=Dgrad(Iend,j) tl_Dgrad(Iend+1,j)=tl_Dgrad(Iend,j) END DO END IF END IF cff=1.0_r8/6.0_r8 DO j=Jstr,Jend DO i=IstrU-1,Iend !^ UFx(i,j)=0.25_r8*(ubar(i ,j,krhs)+ & !^ & ubar(i+1,j,krhs)- & !^ & cff*(grad (i,j)+grad (i+1,j)))* & !^ & (DUon(i,j)+DUon(i+1,j)- & !^ & cff*(Dgrad(i,j)+Dgrad(i+1,j))) !^ tl_UFx(i,j)=0.25_r8* & & ((ubar(i ,j,krhs)+ & & ubar(i+1,j,krhs)- & & cff*(grad (i,j)+grad (i+1,j)))* & & (tl_DUon(i,j)+tl_DUon(i+1,j)- & & cff*(tl_Dgrad(i,j)+tl_Dgrad(i+1,j)))+ & & (tl_ubar(i ,j,krhs)+ & & tl_ubar(i+1,j,krhs)- & & cff*(tl_grad (i,j)+tl_grad (i+1,j)))* & & (DUon(i,j)+DUon(i+1,j)- & & cff*(Dgrad(i,j)+Dgrad(i+1,j)))) END DO END DO ! DO j=Jstrm1,Jendp1 DO i=IstrU,Iend grad(i,j)=ubar(i,j-1,krhs)-2.0_r8*ubar(i,j,krhs)+ & & ubar(i,j+1,krhs) tl_grad(i,j)=tl_ubar(i,j-1,krhs)-2.0_r8*tl_ubar(i,j,krhs)+ & & tl_ubar(i,j+1,krhs) END DO END DO IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Southern_Edge(tile)) THEN DO i=IstrU,Iend grad(i,Jstr-1)=grad(i,Jstr) tl_grad(i,Jstr-1)=tl_grad(i,Jstr) END DO END IF END IF IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Northern_Edge(tile)) THEN DO i=IstrU,Iend grad(i,Jend+1)=grad(i,Jend) tl_grad(i,Jend+1)=tl_grad(i,Jend) END DO END IF END IF DO j=Jstr,Jend+1 DO i=IstrU-1,Iend Dgrad(i,j)=DVom(i-1,j)-2.0_r8*DVom(i,j)+DVom(i+1,j) tl_Dgrad(i,j)=tl_DVom(i-1,j)-2.0_r8*tl_DVom(i,j)+ & & tl_DVom(i+1,j) END DO END DO cff=1.0_r8/6.0_r8 DO j=Jstr,Jend+1 DO i=IstrU,Iend !^ UFe(i,j)=0.25_r8*(ubar(i,j ,krhs)+ & !^ & ubar(i,j-1,krhs)- & !^ & cff*(grad (i,j)+grad (i,j-1)))* & !^ & (DVom(i,j)+DVom(i-1,j)- & !^ & cff*(Dgrad(i,j)+Dgrad(i-1,j))) !^ tl_UFe(i,j)=0.25_r8* & & ((tl_ubar(i,j ,krhs)+ & & tl_ubar(i,j-1,krhs)- & & cff*(tl_grad (i,j)+tl_grad (i,j-1)))* & & (DVom(i,j)+DVom(i-1,j)- & & cff*(Dgrad(i,j)+Dgrad(i-1,j)))+ & & (ubar(i,j ,krhs)+ & & ubar(i,j-1,krhs)- & & cff*(grad (i,j)+grad (i,j-1)))* & & (tl_DVom(i,j)+tl_DVom(i-1,j)- & & cff*(tl_Dgrad(i,j)+tl_Dgrad(i-1,j)))) END DO END DO ! DO j=JstrV,Jend DO i=Istrm1,Iendp1 grad(i,j)=vbar(i-1,j,krhs)-2.0_r8*vbar(i,j,krhs)+ & & vbar(i+1,j,krhs) tl_grad(i,j)=tl_vbar(i-1,j,krhs)-2.0_r8*tl_vbar(i,j,krhs)+ & & tl_vbar(i+1,j,krhs) END DO END DO IF (.not.(CompositeGrid(iwest,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Western_Edge(tile)) THEN DO j=JstrV,Jend grad(Istr-1,j)=grad(Istr,j) tl_grad(Istr-1,j)=tl_grad(Istr,j) END DO END IF END IF IF (.not.(CompositeGrid(ieast,ng).or.EWperiodic(ng))) THEN IF (DOMAIN(ng)%Eastern_Edge(tile)) THEN DO j=JstrV,Jend grad(Iend+1,j)=grad(Iend,j) tl_grad(Iend+1,j)=tl_grad(Iend,j) END DO END IF END IF DO j=JstrV-1,Jend DO i=Istr,Iend+1 Dgrad(i,j)=DUon(i,j-1)-2.0_r8*DUon(i,j)+DUon(i,j+1) tl_Dgrad(i,j)=tl_DUon(i,j-1)-2.0_r8*tl_DUon(i,j)+ & & tl_DUon(i,j+1) END DO END DO cff=1.0_r8/6.0_r8 DO j=JstrV,Jend DO i=Istr,Iend+1 !^ VFx(i,j)=0.25_r8*(vbar(i ,j,krhs)+ & !^ & vbar(i-1,j,krhs)- & !^ & cff*(grad (i,j)+grad (i-1,j)))* & !^ & (DUon(i,j)+DUon(i,j-1)- & !^ & cff*(Dgrad(i,j)+Dgrad(i,j-1))) !^ tl_VFx(i,j)=0.25_r8* & & ((tl_vbar(i ,j,krhs)+ & & tl_vbar(i-1,j,krhs)- & & cff*(tl_grad (i,j)+tl_grad (i-1,j)))* & & (DUon(i,j)+DUon(i,j-1)- & & cff*(Dgrad(i,j)+Dgrad(i,j-1)))+ & & (vbar(i ,j,krhs)+ & & vbar(i-1,j,krhs)- & & cff*(grad (i,j)+grad (i-1,j)))* & & (tl_DUon(i,j)+tl_DUon(i,j-1)- & & cff*(tl_Dgrad(i,j)+tl_Dgrad(i,j-1)))) END DO END DO ! DO j=JstrVm1,Jendp1 DO i=Istr,Iend grad(i,j)=vbar(i,j-1,krhs)-2.0_r8*vbar(i,j,krhs)+ & & vbar(i,j+1,krhs) tl_grad(i,j)=tl_vbar(i,j-1,krhs)-2.0_r8*tl_vbar(i,j,krhs)+ & & tl_vbar(i,j+1,krhs) Dgrad(i,j)=DVom(i,j-1)-2.0_r8*DVom(i,j)+DVom(i,j+1) tl_Dgrad(i,j)=tl_DVom(i,j-1)-2.0_r8*tl_DVom(i,j)+ & & tl_DVom(i,j+1) END DO END DO IF (.not.(CompositeGrid(isouth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Southern_Edge(tile)) THEN DO i=Istr,Iend grad (i,Jstr)=grad (i,Jstr+1) tl_grad (i,Jstr)=tl_grad (i,Jstr+1) Dgrad(i,Jstr)=Dgrad(i,Jstr+1) tl_Dgrad(i,Jstr)=tl_Dgrad(i,Jstr+1) END DO END IF END IF IF (.not.(CompositeGrid(inorth,ng).or.NSperiodic(ng))) THEN IF (DOMAIN(ng)%Northern_Edge(tile)) THEN DO i=Istr,Iend grad (i,Jend+1)=grad (i,Jend) tl_grad (i,Jend+1)=tl_grad (i,Jend) Dgrad(i,Jend+1)=Dgrad(i,Jend) tl_Dgrad(i,Jend+1)=tl_Dgrad(i,Jend) END DO END IF END IF cff=1.0_r8/6.0_r8 DO j=JstrV-1,Jend DO i=Istr,Iend !^ VFe(i,j)=0.25_r8*(vbar(i,j ,krhs)+ & !^ & vbar(i,j+1,krhs)- & !^ & cff*(grad (i,j)+grad (i,j+1)))* & !^ & (DVom(i,j)+DVom(i,j+1)- & !^ & cff*(Dgrad(i,j)+Dgrad(i,j+1))) !^ tl_VFe(i,j)=0.25_r8* & & ((tl_vbar(i,j ,krhs)+ & & tl_vbar(i,j+1,krhs)- & & cff*(tl_grad (i,j)+tl_grad (i,j+1)))* & & (DVom(i,j)+DVom(i,j+1)- & & cff*(Dgrad(i,j)+Dgrad(i,j+1)))+ & & (vbar(i,j ,krhs)+ & & vbar(i,j+1,krhs)- & & cff*(grad (i,j)+grad (i,j+1)))* & & (tl_DVom(i,j)+tl_DVom(i,j+1)- & & cff*(tl_Dgrad(i,j)+tl_Dgrad(i,j+1)))) END DO END DO ! DO j=Jstr,Jend DO i=IstrU,Iend !^ cff1=UFx(i,j)-UFx(i-1,j) !^ tl_cff1=tl_UFx(i,j)-tl_UFx(i-1,j) !^ cff2=UFe(i,j+1)-UFe(i,j) !^ tl_cff2=tl_UFe(i,j+1)-tl_UFe(i,j) !^ fac=cff1+cff2 !^ tl_fac=tl_cff1+tl_cff2 !^ rhs_ubar(i,j)=rhs_ubar(i,j)-fac !^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)-tl_fac END DO END DO DO j=JstrV,Jend DO i=Istr,Iend !^ cff1=VFx(i+1,j)-VFx(i,j) !^ tl_cff1=tl_VFx(i+1,j)-tl_VFx(i,j) !^ cff2=VFe(i,j)-VFe(i,j-1) !^ tl_cff2=tl_VFe(i,j)-tl_VFe(i,j-1) !^ fac=cff1+cff2 !^ tl_fac=tl_cff1+tl_cff2 !^ rhs_vbar(i,j)=rhs_vbar(i,j)-fac !^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)-tl_fac END DO END DO ! !----------------------------------------------------------------------- ! Add in Coriolis term. !----------------------------------------------------------------------- ! DO j=JstrV-1,Jend DO i=IstrU-1,Iend cff=0.5_r8*Drhs(i,j)*fomn(i,j) tl_cff=0.5_r8*tl_Drhs(i,j)*fomn(i,j) !^ UFx(i,j)=cff*(vbar(i,j ,krhs)+ & !^ & vbar(i,j+1,krhs)) !^ tl_UFx(i,j)=tl_cff*(vbar(i,j ,krhs)+ & & vbar(i,j+1,krhs))+ & & cff*(tl_vbar(i,j ,krhs)+ & & tl_vbar(i,j+1,krhs)) !^ VFe(i,j)=cff*(ubar(i ,j,krhs)+ & !^ & ubar(i+1,j,krhs)) !^ tl_VFe(i,j)=tl_cff*(ubar(i ,j,krhs)+ & & ubar(i+1,j,krhs))+ & & cff*(tl_ubar(i ,j,krhs)+ & & tl_ubar(i+1,j,krhs)) END DO END DO DO j=Jstr,Jend DO i=IstrU,Iend !^ fac1=0.5_r8*(UFx(i,j)+UFx(i-1,j)) !^ tl_fac1=0.5_r8*(tl_UFx(i,j)+tl_UFx(i-1,j)) !^ rhs_ubar(i,j)=rhs_ubar(i,j)+fac1 !^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+tl_fac1 END DO END DO DO j=JstrV,Jend DO i=Istr,Iend !^ fac1=0.5_r8*(VFe(i,j)+VFe(i,j-1)) !^ tl_fac1=0.5_r8*(tl_VFe(i,j)+tl_VFe(i,j-1)) !^ rhs_vbar(i,j)=rhs_vbar(i,j)-fac1 !^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)-tl_fac1 END DO END DO ! !----------------------------------------------------------------------- ! Add in curvilinear transformation terms. !----------------------------------------------------------------------- ! DO j=JstrV-1,Jend DO i=IstrU-1,Iend cff1=0.5_r8*(vbar(i,j ,krhs)+ & & vbar(i,j+1,krhs)) tl_cff1=0.5_r8*(tl_vbar(i,j ,krhs)+ & & tl_vbar(i,j+1,krhs)) cff2=0.5_r8*(ubar(i ,j,krhs)+ & & ubar(i+1,j,krhs)) tl_cff2=0.5_r8*(tl_ubar(i ,j,krhs)+ & & tl_ubar(i+1,j,krhs)) cff3=cff1*dndx(i,j) tl_cff3=tl_cff1*dndx(i,j) cff4=cff2*dmde(i,j) tl_cff4=tl_cff2*dmde(i,j) cff=Drhs(i,j)*(cff3-cff4) tl_cff=tl_Drhs(i,j)*(cff3-cff4)+ & & Drhs(i,j)*(tl_cff3-tl_cff4) !^ UFx(i,j)=cff*cff1 !^ tl_UFx(i,j)=tl_cff*cff1+cff*tl_cff1 !^ VFe(i,j)=cff*cff2 !^ tl_VFe(i,j)=tl_cff*cff2+cff*tl_cff2 END DO END DO DO j=Jstr,Jend DO i=IstrU,Iend !^ fac1=0.5_r8*(UFx(i,j)+UFx(i-1,j)) !^ tl_fac1=0.5_r8*(tl_UFx(i,j)+tl_UFx(i-1,j)) !^ rhs_ubar(i,j)=rhs_ubar(i,j)+fac1 !^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+tl_fac1 END DO END DO DO j=JstrV,Jend DO i=Istr,Iend !^ fac1=0.5_r8*(VFe(i,j)+VFe(i,j-1)) !^ tl_fac1=0.5_r8*(tl_VFe(i,j)+tl_VFe(i,j-1)) !^ rhs_vbar(i,j)=rhs_vbar(i,j)-fac1 !^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)-tl_fac1 END DO END DO ! !----------------------------------------------------------------------- ! If horizontal mixing, compute total depth at PSI-points. !----------------------------------------------------------------------- ! DO j=Jstr,Jend+1 DO i=Istr,Iend+1 Drhs_p(i,j)=0.25_r8*(Drhs(i,j )+Drhs(i-1,j )+ & & Drhs(i,j-1)+Drhs(i-1,j-1)) tl_Drhs_p(i,j)=0.25_r8*(tl_Drhs(i,j )+tl_Drhs(i-1,j )+ & & tl_Drhs(i,j-1)+tl_Drhs(i-1,j-1)) END DO END DO ! !----------------------------------------------------------------------- ! Add in horizontal harmonic viscosity. !----------------------------------------------------------------------- ! ! Compute flux-components of the horizontal divergence of the stress ! tensor (m5/s2) in XI- and ETA-directions. ! DO j=JstrV-1,Jend DO i=IstrU-1,Iend !^ cff=visc2_r(i,j)*Drhs(i,j)*0.5_r8* & !^ & (pmon_r(i,j)* & !^ & ((pn(i ,j)+pn(i+1,j))*ubar(i+1,j,krhs)- & !^ & (pn(i-1,j)+pn(i ,j))*ubar(i ,j,krhs))- & !^ & pnom_r(i,j)* & !^ & ((pm(i,j )+pm(i,j+1))*vbar(i,j+1,krhs)- & !^ & (pm(i,j-1)+pm(i,j ))*vbar(i,j ,krhs))) !^ tl_cff=visc2_r(i,j)*0.5_r8* & & (tl_Drhs(i,j)* & & (pmon_r(i,j)* & & ((pn(i ,j)+pn(i+1,j))*ubar(i+1,j,krhs)- & & (pn(i-1,j)+pn(i ,j))*ubar(i ,j,krhs))- & & pnom_r(i,j)* & & ((pm(i,j )+pm(i,j+1))*vbar(i,j+1,krhs)- & & (pm(i,j-1)+pm(i,j ))*vbar(i,j ,krhs)))+ & & Drhs(i,j)* & & (pmon_r(i,j)* & & ((pn(i ,j)+pn(i+1,j))*tl_ubar(i+1,j,krhs)- & & (pn(i-1,j)+pn(i ,j))*tl_ubar(i ,j,krhs))- & & pnom_r(i,j)* & & ((pm(i,j )+pm(i,j+1))*tl_vbar(i,j+1,krhs)- & & (pm(i,j-1)+pm(i,j ))*tl_vbar(i,j ,krhs)))) !^ UFx(i,j)=on_r(i,j)*on_r(i,j)*cff !^ tl_UFx(i,j)=on_r(i,j)*on_r(i,j)*tl_cff !^ VFe(i,j)=om_r(i,j)*om_r(i,j)*cff !^ tl_VFe(i,j)=om_r(i,j)*om_r(i,j)*tl_cff END DO END DO DO j=Jstr,Jend+1 DO i=Istr,Iend+1 !^ cff=visc2_p(i,j)*Drhs_p(i,j)*0.5_r8* & !^ & (pmon_p(i,j)* & !^ & ((pn(i ,j-1)+pn(i ,j))*vbar(i ,j,krhs)- & !^ & (pn(i-1,j-1)+pn(i-1,j))*vbar(i-1,j,krhs))+ & !^ & pnom_p(i,j)* & !^ & ((pm(i-1,j )+pm(i,j ))*ubar(i,j ,krhs)- & !^ & (pm(i-1,j-1)+pm(i,j-1))*ubar(i,j-1,krhs))) !^ tl_cff=visc2_p(i,j)*0.5_r8* & & (tl_Drhs_p(i,j)* & & (pmon_p(i,j)* & & ((pn(i ,j-1)+pn(i ,j))*vbar(i ,j,krhs)- & & (pn(i-1,j-1)+pn(i-1,j))*vbar(i-1,j,krhs))+ & & pnom_p(i,j)* & & ((pm(i-1,j )+pm(i,j ))*ubar(i,j ,krhs)- & & (pm(i-1,j-1)+pm(i,j-1))*ubar(i,j-1,krhs)))+ & & Drhs_p(i,j)* & & (pmon_p(i,j)* & & ((pn(i ,j-1)+pn(i ,j))*tl_vbar(i ,j,krhs)- & & (pn(i-1,j-1)+pn(i-1,j))*tl_vbar(i-1,j,krhs))+ & & pnom_p(i,j)* & & ((pm(i-1,j )+pm(i,j ))*tl_ubar(i,j ,krhs)- & & (pm(i-1,j-1)+pm(i,j-1))*tl_ubar(i,j-1,krhs)))) !^ cff=cff*pmask(i,j) !^ tl_cff=tl_cff*pmask(i,j) !^ UFe(i,j)=om_p(i,j)*om_p(i,j)*cff !^ tl_UFe(i,j)=om_p(i,j)*om_p(i,j)*tl_cff !^ VFx(i,j)=on_p(i,j)*on_p(i,j)*cff !^ tl_VFx(i,j)=on_p(i,j)*on_p(i,j)*tl_cff END DO END DO ! ! Add in harmonic viscosity. ! DO j=Jstr,Jend DO i=IstrU,Iend !^ cff1=0.5_r8*(pn(i-1,j)+pn(i,j))*(UFx(i,j )-UFx(i-1,j)) !^ tl_cff1=0.5_r8*(pn(i-1,j)+pn(i,j))* & & (tl_UFx(i,j )-tl_UFx(i-1,j)) !^ cff2=0.5_r8*(pm(i-1,j)+pm(i,j))*(UFe(i,j+1)-UFe(i ,j)) !^ tl_cff2=0.5_r8*(pm(i-1,j)+pm(i,j))* & & (tl_UFe(i,j+1)-tl_UFe(i ,j)) !^ fac=cff1+cff2 !^ tl_fac=tl_cff1+tl_cff2 !^ rhs_ubar(i,j)=rhs_ubar(i,j)+fac !^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+tl_fac END DO END DO DO j=JstrV,Jend DO i=Istr,Iend !^ cff1=0.5_r8*(pn(i,j-1)+pn(i,j))*(VFx(i+1,j)-VFx(i,j )) !^ tl_cff1=0.5_r8*(pn(i,j-1)+pn(i,j))* & & (tl_VFx(i+1,j)-tl_VFx(i,j )) !^ cff2=0.5_r8*(pm(i,j-1)+pm(i,j))*(VFe(i ,j)-VFe(i,j-1)) !^ tl_cff2=0.5_r8*(pm(i,j-1)+pm(i,j))* & & (tl_VFe(i ,j)-tl_VFe(i,j-1)) !^ fac=cff1-cff2 !^ tl_fac=tl_cff1-tl_cff2 !^ rhs_vbar(i,j)=rhs_vbar(i,j)+fac !^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)+tl_fac END DO END DO ! !----------------------------------------------------------------------- ! Add in nudging of 2D momentum climatology. !----------------------------------------------------------------------- ! IF (LnudgeM2CLM(ng)) THEN DO j=Jstr,Jend DO i=IstrU,Iend cff=0.25_r8*(CLIMA(ng)%M2nudgcof(i-1,j)+ & & CLIMA(ng)%M2nudgcof(i ,j))* & & om_u(i,j)*on_u(i,j) !^ rhs_ubar(i,j)=rhs_ubar(i,j)+ & !^ & cff*(Drhs(i-1,j)+Drhs(i,j))* & !^ & (CLIMA(ng)%ubarclm(i,j)- & !^ & ubar(i,j,krhs)) !^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+ & & cff*((Drhs(i-1,j)+Drhs(i,j))* & & (-tl_ubar(i,j,krhs))+ & & (tl_Drhs(i-1,j)+tl_Drhs(i,j))* & & (CLIMA(ng)%ubarclm(i,j)- & & ubar(i,j,krhs))) END DO END DO DO j=JstrV,Jend DO i=Istr,Iend cff=0.25_r8*(CLIMA(ng)%M2nudgcof(i,j-1)+ & & CLIMA(ng)%M2nudgcof(i,j ))* & & om_v(i,j)*on_v(i,j) !^ rhs_vbar(i,j)=rhs_vbar(i,j)+ & !^ & cff*(Drhs(i,j-1)+Drhs(i,j))* & !^ & (CLIMA(ng)%vbarclm(i,j)- & !^ & vbar(i,j,krhs)) !^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)+ & & cff*((Drhs(i,j-1)+Drhs(i,j))* & & (-tl_vbar(i,j,krhs))+ & & (tl_Drhs(i,j-1)+tl_Drhs(i,j))* & & (CLIMA(ng)%vbarclm(i,j)- & & vbar(i,j,krhs))) END DO END DO END IF ! !----------------------------------------------------------------------- ! Coupling between 2D and 3D equations. !----------------------------------------------------------------------- ! ! Before the predictor step of the first barotropic time-step, ! arrays "rufrc" and "rvfrc" contain the vertical integrals of ! the 3D right-hand-side terms for momentum equations (including ! surface and bottom stresses, if so prescribed). ! ! Convert them into forcing terms by subtracting the fast time ! "rhs_ubar" and "rhs_vbar" from them; Also, immediately apply ! these forcing terms "rhs_ubar" and "rhs_vbar". ! ! From now on, these newly computed forcing terms will remain ! constant during the fast time stepping and will added to ! "rhs_ubar" and "rhs_vbar" during all subsequent time steps. ! IF (iif(ng).eq.1.and.PREDICTOR_2D_STEP(ng)) THEN IF (iic(ng).eq.ntfirst(ng)) THEN DO j=Jstr,Jend DO i=IstrU,Iend !^ rufrc(i,j)=rufrc(i,j)-rhs_ubar(i,j) !^ tl_rufrc(i,j)=tl_rufrc(i,j)-tl_rhs_ubar(i,j) !^ rhs_ubar(i,j)=rhs_ubar(i,j)+rufrc(i,j) !^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+tl_rufrc(i,j) !^ ru(i,j,0,nstp)=rufrc(i,j) !^ tl_ru(i,j,0,nstp)=tl_rufrc(i,j) END DO END DO DO j=JstrV,Jend DO i=Istr,Iend !^ rvfrc(i,j)=rvfrc(i,j)-rhs_vbar(i,j) !^ tl_rvfrc(i,j)=tl_rvfrc(i,j)-tl_rhs_vbar(i,j) !^ rhs_vbar(i,j)=rhs_vbar(i,j)+rvfrc(i,j) !^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)+tl_rvfrc(i,j) !^ rv(i,j,0,nstp)=rvfrc(i,j) !^ tl_rv(i,j,0,nstp)=tl_rvfrc(i,j) END DO END DO ELSE IF (iic(ng).eq.(ntfirst(ng)+1)) THEN DO j=Jstr,Jend DO i=IstrU,Iend !^ rufrc(i,j)=rufrc(i,j)-rhs_ubar(i,j) !^ tl_rufrc(i,j)=tl_rufrc(i,j)-tl_rhs_ubar(i,j) !^ rhs_ubar(i,j)=rhs_ubar(i,j)+ & !^ & 1.5_r8*rufrc(i,j)-0.5_r8*ru(i,j,0,nnew) !^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+ & & 1.5_r8*tl_rufrc(i,j)- & & 0.5_r8*tl_ru(i,j,0,nnew) !^ ru(i,j,0,nstp)=rufrc(i,j) !^ tl_ru(i,j,0,nstp)=tl_rufrc(i,j) END DO END DO DO j=JstrV,Jend DO i=Istr,Iend !^ rvfrc(i,j)=rvfrc(i,j)-rhs_vbar(i,j) !^ tl_rvfrc(i,j)=tl_rvfrc(i,j)-tl_rhs_vbar(i,j) !^ rhs_vbar(i,j)=rhs_vbar(i,j)+ & !^ & 1.5_r8*rvfrc(i,j)-0.5_r8*rv(i,j,0,nnew) !^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)+ & & 1.5_r8*tl_rvfrc(i,j)- & & 0.5_r8*tl_rv(i,j,0,nnew) !^ rv(i,j,0,nstp)=rvfrc(i,j) !^ tl_rv(i,j,0,nstp)=tl_rvfrc(i,j) END DO END DO ELSE cff1=23.0_r8/12.0_r8 cff2=16.0_r8/12.0_r8 cff3= 5.0_r8/12.0_r8 DO j=Jstr,Jend DO i=IstrU,Iend !^ rufrc(i,j)=rufrc(i,j)-rhs_ubar(i,j) !^ tl_rufrc(i,j)=tl_rufrc(i,j)-tl_rhs_ubar(i,j) !^ rhs_ubar(i,j)=rhs_ubar(i,j)+ & !^ & cff1*rufrc(i,j)- & !^ & cff2*ru(i,j,0,nnew)+ & !^ & cff3*ru(i,j,0,nstp) !^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+ & & cff1*tl_rufrc(i,j)- & & cff2*tl_ru(i,j,0,nnew)+ & & cff3*tl_ru(i,j,0,nstp) !^ ru(i,j,0,nstp)=rufrc(i,j) !^ tl_ru(i,j,0,nstp)=tl_rufrc(i,j) END DO END DO DO j=JstrV,Jend DO i=Istr,Iend !^ rvfrc(i,j)=rvfrc(i,j)-rhs_vbar(i,j) !^ tl_rvfrc(i,j)=tl_rvfrc(i,j)-tl_rhs_vbar(i,j) !^ rhs_vbar(i,j)=rhs_vbar(i,j)+ & !^ & cff1*rvfrc(i,j)- & !^ & cff2*rv(i,j,0,nnew)+ & !^ & cff3*rv(i,j,0,nstp) !^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)+ & & cff1*tl_rvfrc(i,j)- & & cff2*tl_rv(i,j,0,nnew)+ & & cff3*tl_rv(i,j,0,nstp) !^ rv(i,j,0,nstp)=rvfrc(i,j) !^ tl_rv(i,j,0,nstp)=tl_rvfrc(i,j) END DO END DO END IF ELSE DO j=Jstr,Jend DO i=IstrU,Iend !^ rhs_ubar(i,j)=rhs_ubar(i,j)+rufrc(i,j) !^ tl_rhs_ubar(i,j)=tl_rhs_ubar(i,j)+tl_rufrc(i,j) END DO END DO DO j=JstrV,Jend DO i=Istr,Iend !^ rhs_vbar(i,j)=rhs_vbar(i,j)+rvfrc(i,j) !^ tl_rhs_vbar(i,j)=tl_rhs_vbar(i,j)+tl_rvfrc(i,j) END DO END DO END IF ! !======================================================================= ! Time step 2D momentum equations. !======================================================================= ! ! Compute total water column depth. ! DO j=JstrV-1,Jend DO i=IstrU-1,Iend Dstp(i,j)=zeta(i,j,kstp)+h(i,j) tl_Dstp(i,j)=tl_zeta(i,j,kstp)+tl_h(i,j) END DO END DO ! ! During the first time-step, the predictor step is Forward-Euler ! and the corrector step is Backward-Euler. Otherwise, the predictor ! step is Leap-frog and the corrector step is Adams-Moulton. ! IF (iif(ng).eq.1) THEN cff1=0.5_r8*dtfast(ng) DO j=Jstr,Jend DO i=IstrU,Iend cff=(pm(i,j)+pm(i-1,j))*(pn(i,j)+pn(i-1,j)) fac=1.0_r8/(Dnew(i,j)+Dnew(i-1,j)) tl_fac=-fac*fac*(tl_Dnew(i,j)+tl_Dnew(i-1,j)) !^ ubar(i,j,knew)=(ubar(i,j,kstp)* & !^ & (Dstp(i,j)+Dstp(i-1,j))+ & !^ & cff*cff1*rhs_ubar(i,j))*fac !^ tl_ubar(i,j,knew)=(tl_ubar(i,j,kstp)* & & (Dstp(i,j)+Dstp(i-1,j))+ & & ubar(i,j,kstp)* & & (tl_Dstp(i,j)+tl_Dstp(i-1,j))+ & & cff*cff1*tl_rhs_ubar(i,j))*fac+ & & (ubar(i,j,kstp)* & & (Dstp(i,j)+Dstp(i-1,j))+ & & cff*cff1*rhs_ubar(i,j))*tl_fac !^ ubar(i,j,knew)=ubar(i,j,knew)*umask(i,j) !^ tl_ubar(i,j,knew)=tl_ubar(i,j,knew)*umask(i,j) END DO END DO DO j=JstrV,Jend DO i=Istr,Iend cff=(pm(i,j)+pm(i,j-1))*(pn(i,j)+pn(i,j-1)) fac=1.0_r8/(Dnew(i,j)+Dnew(i,j-1)) tl_fac=-fac*fac*(tl_Dnew(i,j)+tl_Dnew(i,j-1)) !^ vbar(i,j,knew)=(vbar(i,j,kstp)* & !^ & (Dstp(i,j)+Dstp(i,j-1))+ & !^ & cff*cff1*rhs_vbar(i,j))*fac !^ tl_vbar(i,j,knew)=(tl_vbar(i,j,kstp)* & & (Dstp(i,j)+Dstp(i,j-1))+ & & vbar(i,j,kstp)* & & (tl_Dstp(i,j)+tl_Dstp(i,j-1))+ & & cff*cff1*tl_rhs_vbar(i,j))*fac+ & & (vbar(i,j,kstp)* & & (Dstp(i,j)+Dstp(i,j-1))+ & & cff*cff1*rhs_vbar(i,j))*tl_fac !^ vbar(i,j,knew)=vbar(i,j,knew)*vmask(i,j) !^ tl_vbar(i,j,knew)=tl_vbar(i,j,knew)*vmask(i,j) END DO END DO ELSE IF (PREDICTOR_2D_STEP(ng)) THEN cff1=dtfast(ng) DO j=Jstr,Jend DO i=IstrU,Iend cff=(pm(i,j)+pm(i-1,j))*(pn(i,j)+pn(i-1,j)) fac=1.0_r8/(Dnew(i,j)+Dnew(i-1,j)) tl_fac=-fac*fac*(tl_Dnew(i,j)+tl_Dnew(i-1,j)) !^ ubar(i,j,knew)=(ubar(i,j,kstp)* & !^ & (Dstp(i,j)+Dstp(i-1,j))+ & !^ & cff*cff1*rhs_ubar(i,j))*fac !^ tl_ubar(i,j,knew)=(tl_ubar(i,j,kstp)* & & (Dstp(i,j)+Dstp(i-1,j))+ & & ubar(i,j,kstp)* & & (tl_Dstp(i,j)+tl_Dstp(i-1,j))+ & & cff*cff1*tl_rhs_ubar(i,j))*fac+ & & (ubar(i,j,kstp)* & & (Dstp(i,j)+Dstp(i-1,j))+ & & cff*cff1*rhs_ubar(i,j))*tl_fac !^ ubar(i,j,knew)=ubar(i,j,knew)*umask(i,j) !^ tl_ubar(i,j,knew)=tl_ubar(i,j,knew)*umask(i,j) END DO END DO DO j=JstrV,Jend DO i=Istr,Iend cff=(pm(i,j)+pm(i,j-1))*(pn(i,j)+pn(i,j-1)) fac=1.0_r8/(Dnew(i,j)+Dnew(i,j-1)) tl_fac=-fac*fac*(tl_Dnew(i,j)+tl_Dnew(i,j-1)) !^ vbar(i,j,knew)=(vbar(i,j,kstp)* & !^ & (Dstp(i,j)+Dstp(i,j-1))+ & !^ & cff*cff1*rhs_vbar(i,j))*fac !^ tl_vbar(i,j,knew)=(tl_vbar(i,j,kstp)* & & (Dstp(i,j)+Dstp(i,j-1))+ & & vbar(i,j,kstp)* & & (tl_Dstp(i,j)+tl_Dstp(i,j-1))+ & & cff*cff1*tl_rhs_vbar(i,j))*fac+ & & (vbar(i,j,kstp)* & & (Dstp(i,j)+Dstp(i,j-1))+ & & cff*cff1*rhs_vbar(i,j))*tl_fac !^ vbar(i,j,knew)=vbar(i,j,knew)*vmask(i,j) !^ tl_vbar(i,j,knew)=tl_vbar(i,j,knew)*vmask(i,j) END DO END DO ELSE IF (CORRECTOR_2D_STEP) THEN cff1=0.5_r8*dtfast(ng)*5.0_r8/12.0_r8 cff2=0.5_r8*dtfast(ng)*8.0_r8/12.0_r8 cff3=0.5_r8*dtfast(ng)*1.0_r8/12.0_r8 DO j=Jstr,Jend DO i=IstrU,Iend cff=(pm(i,j)+pm(i-1,j))*(pn(i,j)+pn(i-1,j)) fac=1.0_r8/(Dnew(i,j)+Dnew(i-1,j)) tl_fac=-fac*fac*(tl_Dnew(i,j)+tl_Dnew(i-1,j)) !^ ubar(i,j,knew)=(ubar(i,j,kstp)* & !^ & (Dstp(i,j)+Dstp(i-1,j))+ & !^ & cff*(cff1*rhs_ubar(i,j)+ & !^ & cff2*rubar(i,j,kstp)- & !^ & cff3*rubar(i,j,ptsk)))*fac !^ tl_ubar(i,j,knew)=(tl_ubar(i,j,kstp)* & & (Dstp(i,j)+Dstp(i-1,j))+ & & ubar(i,j,kstp)* & & (tl_Dstp(i,j)+tl_Dstp(i-1,j))+ & & cff*(cff1*tl_rhs_ubar(i,j)+ & & cff2*tl_rubar(i,j,kstp)- & & cff3*tl_rubar(i,j,ptsk)))*fac+ & & (ubar(i,j,kstp)* & & (Dstp(i,j)+Dstp(i-1,j))+ & & cff*(cff1*rhs_ubar(i,j)+ & & cff2*rubar(i,j,kstp)- & & cff3*rubar(i,j,ptsk)))*tl_fac !^ ubar(i,j,knew)=ubar(i,j,knew)*umask(i,j) !^ tl_ubar(i,j,knew)=tl_ubar(i,j,knew)*umask(i,j) END DO END DO DO j=JstrV,Jend DO i=Istr,Iend cff=(pm(i,j)+pm(i,j-1))*(pn(i,j)+pn(i,j-1)) fac=1.0_r8/(Dnew(i,j)+Dnew(i,j-1)) tl_fac=-fac*fac*(tl_Dnew(i,j)+tl_Dnew(i,j-1)) !^ vbar(i,j,knew)=(vbar(i,j,kstp)* & !^ & (Dstp(i,j)+Dstp(i,j-1))+ & !^ & cff*(cff1*rhs_vbar(i,j)+ & !^ & cff2*rvbar(i,j,kstp)- & !^ & cff3*rvbar(i,j,ptsk)))*fac !^ tl_vbar(i,j,knew)=(tl_vbar(i,j,kstp)* & & (Dstp(i,j)+Dstp(i,j-1))+ & & vbar(i,j,kstp)* & & (tl_Dstp(i,j)+tl_Dstp(i,j-1))+ & & cff*(cff1*tl_rhs_vbar(i,j)+ & & cff2*tl_rvbar(i,j,kstp)- & & cff3*tl_rvbar(i,j,ptsk)))*fac+ & & (vbar(i,j,kstp)* & & (Dstp(i,j)+Dstp(i,j-1))+ & & cff*(cff1*rhs_vbar(i,j)+ & & cff2*rvbar(i,j,kstp)- & & cff3*rvbar(i,j,ptsk)))*tl_fac !^ vbar(i,j,knew)=vbar(i,j,knew)*vmask(i,j) !^ tl_vbar(i,j,knew)=tl_vbar(i,j,knew)*vmask(i,j) END DO END DO END IF ! ! If predictor step, load right-side-term into shared arrays for ! future use during the subsequent corrector step. ! IF (PREDICTOR_2D_STEP(ng)) THEN DO j=Jstr,Jend DO i=IstrU,Iend !^ rubar(i,j,krhs)=rhs_ubar(i,j) !^ tl_rubar(i,j,krhs)=tl_rhs_ubar(i,j) END DO END DO DO j=JstrV,Jend DO i=Istr,Iend !^ rvbar(i,j,krhs)=rhs_vbar(i,j) !^ tl_rvbar(i,j,krhs)=tl_rhs_vbar(i,j) END DO END DO END IF ! !----------------------------------------------------------------------- ! Apply lateral boundary conditions. !----------------------------------------------------------------------- ! !^ CALL u2dbc_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & krhs, kstp, knew, & !^ & ubar, vbar, zeta) !^ CALL tl_u2dbc_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & krhs, kstp, knew, & & ubar, vbar, zeta, & & tl_ubar, tl_vbar, tl_zeta) !^ CALL v2dbc_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & IminS, ImaxS, JminS, JmaxS, & !^ & krhs, kstp, knew, & !^ & ubar, vbar, zeta) !^ CALL tl_v2dbc_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & krhs, kstp, knew, & & ubar, vbar, zeta, & & tl_ubar, tl_vbar, tl_zeta) ! ! Compute integral mass flux across open boundaries and adjust ! for volume conservation. ! IF (ANY(tl_VolCons(:,ng))) THEN CALL tl_obc_flux_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & knew, & & umask, vmask, & & h, tl_h, om_v, on_u, & & ubar, vbar, zeta, & & tl_ubar, tl_vbar, tl_zeta) END IF ! !----------------------------------------------------------------------- ! Apply momentum transport point sources (like river runoff), if any. ! ! Dsrc(is) = 0, flow across grid cell u-face (positive or negative) ! Dsrc(is) = 1, flow across grid cell v-face (positive or negative) !----------------------------------------------------------------------- ! IF (LuvSrc(ng)) THEN DO is=1,Nsrc(ng) i=SOURCES(ng)%Isrc(is) j=SOURCES(ng)%Jsrc(is) IF (((IstrR.le.i).and.(i.le.IendR)).and. & & ((JstrR.le.j).and.(j.le.JendR))) THEN IF (INT(SOURCES(ng)%Dsrc(is)).eq.0) THEN cff=1.0_r8/(on_u(i,j)* & & 0.5_r8*(zeta(i-1,j,knew)+h(i-1,j)+ & & zeta(i ,j,knew)+h(i ,j))) tl_cff=-cff*cff*on_u(i,j)* & & 0.5_r8*(tl_zeta(i-1,j,knew)+tl_h(i-1,j)+ & & tl_zeta(i ,j,knew)+tl_h(i ,j)) !^ ubar(i,j,knew)=SOURCES(ng)%Qbar(is)*cff !^ tl_ubar(i,j,knew)=SOURCES(ng)%tl_Qbar(is)*cff+ & & SOURCES(ng)%Qbar(is)*tl_cff ELSE IF (INT(SOURCES(ng)%Dsrc(is)).eq.1) THEN cff=1.0_r8/(om_v(i,j)* & & 0.5_r8*(zeta(i,j-1,knew)+h(i,j-1)+ & & zeta(i,j ,knew)+h(i,j ))) tl_cff=-cff*cff*om_v(i,j)* & & 0.5_r8*(tl_zeta(i,j-1,knew)+tl_h(i,j-1)+ & & tl_zeta(i,j ,knew)+tl_h(i,j )) !^ vbar(i,j,knew)=SOURCES(ng)%Qbar(is)*cff !^ tl_vbar(i,j,knew)=SOURCES(ng)%tl_Qbar(is)*cff+ & & SOURCES(ng)%Qbar(is)*tl_cff END IF END IF END DO END IF ! !----------------------------------------------------------------------- ! Exchange boundary information. !----------------------------------------------------------------------- ! IF (EWperiodic(ng).or.NSperiodic(ng)) THEN !^ CALL exchange_u2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & ubar(:,:,knew)) !^ CALL exchange_u2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & tl_ubar(:,:,knew)) !^ CALL exchange_v2d_tile (ng, tile, & !^ & LBi, UBi, LBj, UBj, & !^ & vbar(:,:,knew)) !^ CALL exchange_v2d_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & tl_vbar(:,:,knew)) END IF !^ CALL mp_exchange2d (ng, tile, iNLM, 2, & !^ & LBi, UBi, LBj, UBj, & !^ & NghostPoints, & !^ & EWperiodic(ng), NSperiodic(ng), & !^ & ubar(:,:,knew), & !^ & vbar(:,:,knew)) !^ CALL mp_exchange2d (ng, tile, iTLM, 2, & & LBi, UBi, LBj, UBj, & & NghostPoints, & & EWperiodic(ng), NSperiodic(ng), & & tl_ubar(:,:,knew), & & tl_vbar(:,:,knew)) ! RETURN END SUBROUTINE tl_step2d_tile END MODULE tl_step2d_mod