MODULE my25_prestep_mod
!
!git $Id$
!svn $Id: my25_prestep.F 1151 2023-02-09 03:08:53Z arango $
!=======================================================================
! Copyright (c) 2002-2023 The ROMS/TOMS Group !
! Licensed under a MIT/X style license !
! See License_ROMS.md Hernan G. Arango !
!========================================== Alexander F. Shchepetkin ===
! !
! This routine perfoms the predictor step for turbulent kinetic !
! energy prognostic variables, tke and gls. A NON-conservative, !
! but constancy preserving, auxiliary advective substep for tke !
! gls equations is carried out. The result of this substep will !
! be used to compute advective terms in the corrector substep. !
! No dissipation terms are included here. !
! !
!=======================================================================
!
implicit none
!
PRIVATE
PUBLIC :: my25_prestep
!
CONTAINS
!
!***********************************************************************
SUBROUTINE my25_prestep (ng, tile)
!***********************************************************************
!
USE mod_param
USE mod_grid
USE mod_mixing
USE mod_ocean
USE mod_stepping
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile
!
! Local variable declarations.
!
character (len=*), parameter :: MyFile = &
& "ROMS/Nonlinear/my25_prestep.F"
!
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, iNLM, 20, 51, MyFile)
CALL my25_prestep_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& nstp(ng), nnew(ng), &
& GRID(ng) % umask, &
& GRID(ng) % vmask, &
& GRID(ng) % Huon, &
& GRID(ng) % Hvom, &
& GRID(ng) % Hz, &
& GRID(ng) % pm, &
& GRID(ng) % pn, &
& OCEAN(ng) % W, &
& MIXING(ng) % gls, &
& MIXING(ng) % tke)
CALL wclock_off (ng, iNLM, 20, 70, MyFile)
!
RETURN
END SUBROUTINE my25_prestep
!
!***********************************************************************
SUBROUTINE my25_prestep_tile (ng, tile, &
& LBi, UBi, LBj, UBj, &
& IminS, ImaxS, JminS, JmaxS, &
& nstp, nnew, &
& umask, vmask, &
& Huon, Hvom, Hz, pm, pn, W, &
& gls, tke)
!***********************************************************************
!
USE mod_param
USE mod_ncparam
USE mod_scalars
!
USE exchange_3d_mod, ONLY : exchange_w3d_tile
USE mp_exchange_mod, ONLY : mp_exchange3d
USE tkebc_mod, ONLY : tkebc_tile
!
! Imported variable declarations.
!
integer, intent(in) :: ng, tile
integer, intent(in) :: LBi, UBi, LBj, UBj
integer, intent(in) :: IminS, ImaxS, JminS, JmaxS
integer, intent(in) :: nstp, nnew
!
real(r8), intent(in) :: umask(LBi:,LBj:)
real(r8), intent(in) :: vmask(LBi:,LBj:)
real(r8), intent(in) :: Huon(LBi:,LBj:,:)
real(r8), intent(in) :: Hvom(LBi:,LBj:,:)
real(r8), intent(in) :: Hz(LBi:,LBj:,:)
real(r8), intent(in) :: pm(LBi:,LBj:)
real(r8), intent(in) :: pn(LBi:,LBj:)
real(r8), intent(in) :: W(LBi:,LBj:,0:)
real(r8), intent(inout) :: gls(LBi:,LBj:,0:,:)
real(r8), intent(inout) :: tke(LBi:,LBj:,0:,:)
!
! Local variable declarations.
!
integer :: i, indx, j, k
real(r8), parameter :: Gamma = 1.0_r8/6.0_r8
real(r8) :: cff, cff1, cff2, cff3, cff4
real(r8), dimension(IminS:ImaxS,N(ng)) :: CF
real(r8), dimension(IminS:ImaxS,N(ng)) :: FC
real(r8), dimension(IminS:ImaxS,N(ng)) :: FCL
real(r8), dimension(IminS:ImaxS,JminS:JmaxS,N(ng)) :: Hz_half
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: EF
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FE
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FEL
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FX
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: FXL
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: XF
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: grad
real(r8), dimension(IminS:ImaxS,JminS:JmaxS) :: gradL
!
!-----------------------------------------------------------------------
! 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
!
!-----------------------------------------------------------------------
! Predictor step for advection of turbulent kinetic energy variables.
!-----------------------------------------------------------------------
!
! Start computation of auxiliary time step fields tke(:,:,:,n+1/2) and
! gls(:,:,:,n+1/2) with computation of horizontal advection terms and
! auxiliary grid-box height field Hz_new()=Hz(:,:,k+1/2,n+1/2);
! This is effectivey an LF step with subsequent interpolation of the
! result half step back, using AM3 weights. The LF step and
! interpolation are perfomed as a single operation, which results in
! weights cff1,cff2,cff3 below.
!
! Either centered fourth-order accurate or standard second order
! accurate versions are supported.
!
! At the same time prepare for corrector step for tke,gls: set tke,
! gls(:,:,:,nnew) to tke, gls(:,:,:,nstp) multiplied by the
! corresponding grid-box height. This needs done at this time because
! array Hz(:,:,:) will overwritten after 2D time stepping with the
! values computed from zeta(:,:,n+1) rather than zeta(:,:,n), so that
! the old-time-step Hz will be no longer awailable.
!
DO k=1,N(ng)-1
!
! Fourth-order, centered differences advection.
!
DO j=Jstr,Jend
DO i=Istrm1,Iendp2
grad (i,j)=(tke(i,j,k,nstp)-tke(i-1,j,k,nstp))
grad (i,j)=grad (i,j)*umask(i,j)
gradL(i,j)=(gls(i,j,k,nstp)-gls(i-1,j,k,nstp))
gradL(i,j)=gradL(i,j)*umask(i,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-1,j)=grad (Istr,j)
gradL(Istr-1,j)=gradL(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=Jstr,Jend
grad (Iend+2,j)=grad (Iend+1,j)
gradL(Iend+2,j)=gradL(Iend+1,j)
END DO
END IF
END IF
cff=1.0_r8/6.0_r8
DO j=Jstr,Jend
DO i=Istr,Iend+1
XF(i,j)=0.5_r8*(Huon(i,j,k)+Huon(i,j,k+1))
FX (i,j)=XF(i,j)* &
& 0.5_r8*(tke(i-1,j,k,nstp)+tke(i,j,k,nstp)- &
& cff*(grad (i+1,j)-grad (i-1,j)))
FXL(i,j)=XF(i,j)* &
& 0.5_r8*(gls(i-1,j,k,nstp)+gls(i,j,k,nstp)- &
& cff*(gradL(i+1,j)-gradL(i-1,j)))
END DO
END DO
!
DO j=Jstrm1,Jendp2
DO i=Istr,Iend
grad (i,j)=(tke(i,j,k,nstp)-tke(i,j-1,k,nstp))
grad (i,j)=grad (i,j)*vmask(i,j)
gradL(i,j)=(gls(i,j,k,nstp)-gls(i,j-1,k,nstp))
gradL(i,j)=gradL(i,j)*vmask(i,j)
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-1)=grad (i,Jstr)
gradL(i,Jstr-1)=gradL(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=Istr,Iend
grad (i,Jend+2)=grad (i,Jend+1)
gradL(i,Jend+2)=gradL(i,Jend+1)
END DO
END IF
END IF
cff=1.0_r8/6.0_r8
DO j=Jstr,Jend+1
DO i=Istr,Iend
EF(i,j)=0.5_r8*(Hvom(i,j,k)+Hvom(i,j,k+1))
FE (i,j)=EF(i,j)* &
& 0.5_r8*(tke(i,j-1,k,nstp)+tke(i,j,k,nstp)- &
& cff*(grad (i,j+1)-grad (i,j-1)))
FEL(i,j)=EF(i,j)* &
& 0.5_r8*(gls(i,j-1,k,nstp)+gls(i,j,k,nstp)- &
& cff*(gradL(i,j+1)-gradL(i,j-1)))
END DO
END DO
!
! Time-step horizontal advection.
!
IF (iic(ng).eq.ntfirst(ng)) THEN
cff1=1.0_r8
cff2=0.0_r8
cff3=0.5_r8*dt(ng)
indx=nstp
ELSE
cff1=0.5_r8+Gamma
cff2=0.5_r8-Gamma
cff3=(1.0_r8-Gamma)*dt(ng)
indx=3-nstp
END IF
DO j=Jstr,Jend
DO i=Istr,Iend
cff=0.5_r8*(Hz(i,j,k)+Hz(i,j,k+1))
cff4=cff3*pm(i,j)*pn(i,j)
Hz_half(i,j,k)=cff-cff4*(XF(i+1,j)-XF(i,j)+ &
& EF(i,j+1)-EF(i,j))
tke(i,j,k,3)=cff*(cff1*tke(i,j,k,nstp)+ &
& cff2*tke(i,j,k,indx))- &
& cff4*(FX (i+1,j)-FX (i,j)+ &
& FE (i,j+1)-FE (i,j))
gls(i,j,k,3)=cff*(cff1*gls(i,j,k,nstp)+ &
& cff2*gls(i,j,k,indx))- &
& cff4*(FXL(i+1,j)-FXL(i,j)+ &
& FEL(i,j+1)-FEL(i,j))
tke(i,j,k,nnew)=cff*tke(i,j,k,nstp)
gls(i,j,k,nnew)=cff*gls(i,j,k,nstp)
END DO
END DO
END DO
!
! Compute vertical advection term.
!
DO j=Jstr,Jend
cff1=7.0_r8/12.0_r8
cff2=1.0_r8/12.0_r8
DO k=2,N(ng)-1
DO i=Istr,Iend
CF(i,k)=0.5_r8*(W(i,j,k)+W(i,j,k-1))
FC (i,k)=CF(i,k)*(cff1*(tke(i,j,k-1,nstp)+ &
& tke(i,j,k ,nstp))- &
& cff2*(tke(i,j,k-2,nstp)+ &
& tke(i,j,k+1,nstp)))
FCL(i,k)=CF(i,k)*(cff1*(gls(i,j,k-1,nstp)+ &
& gls(i,j,k ,nstp))- &
& cff2*(gls(i,j,k-2,nstp)+ &
& gls(i,j,k+1,nstp)))
END DO
END DO
cff1=1.0_r8/3.0_r8
cff2=5.0_r8/6.0_r8
cff3=1.0_r8/6.0_r8
DO i=Istr,Iend
CF(i,1)=0.5*(W(i,j,0)+W(i,j,1))
FC (i,1)=CF(i,1)*(cff1*tke(i,j,0,nstp)+ &
& cff2*tke(i,j,1,nstp)- &
& cff3*tke(i,j,2,nstp))
FCL(i,1)=CF(i,1)*(cff1*gls(i,j,0,nstp)+ &
& cff2*gls(i,j,1,nstp)- &
& cff3*gls(i,j,2,nstp))
CF(i,N(ng))=0.5*(W(i,j,N(ng))+W(i,j,N(ng)-1))
FC (i,N(ng))=CF(i,N(ng))*(cff1*tke(i,j,N(ng) ,nstp)+ &
& cff2*tke(i,j,N(ng)-1,nstp)- &
& cff3*tke(i,j,N(ng)-2,nstp))
FCL(i,N(ng))=CF(i,N(ng))*(cff1*gls(i,j,N(ng) ,nstp)+ &
& cff2*gls(i,j,N(ng)-1,nstp)- &
& cff3*gls(i,j,N(ng)-2,nstp))
END DO
!
! Time-step vertical advection term.
!
IF (iic(ng).eq.ntfirst(ng)) THEN
cff3=0.5_r8*dt(ng)
ELSE
cff3=(1.0_r8-Gamma)*dt(ng)
END IF
DO k=1,N(ng)-1
DO i=Istr,Iend
cff4=cff3*pm(i,j)*pn(i,j)
Hz_half(i,j,k)=Hz_half(i,j,k)-cff4*(CF(i,k+1)-CF(i,k))
cff1=1.0_r8/Hz_half(i,j,k)
tke(i,j,k,3)=cff1*(tke(i,j,k,3)- &
& cff4*(FC (i,k+1)-FC (i,k)))
gls(i,j,k,3)=cff1*(gls(i,j,k,3)- &
& cff4*(FCL(i,k+1)-FCL(i,k)))
END DO
END DO
END DO
!
! Apply lateral boundary conditions.
!
CALL tkebc_tile (ng, tile, &
& LBi, UBi, LBj, UBj, N(ng), &
& IminS, ImaxS, JminS, JmaxS, &
& 3, nstp, &
& gls, tke)
!
IF (EWperiodic(ng).or.NSperiodic(ng)) THEN
CALL exchange_w3d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, 0, N(ng), &
& tke(:,:,:,3))
CALL exchange_w3d_tile (ng, tile, &
& LBi, UBi, LBj, UBj, 0, N(ng), &
& gls(:,:,:,3))
END IF
CALL mp_exchange3d (ng, tile, iNLM, 2, &
& LBi, UBi, LBj, UBj, 0, N(ng), &
& NghostPoints, &
& EWperiodic(ng), NSperiodic(ng), &
& tke(:,:,:,3), &
& gls(:,:,:,3))
!
RETURN
END SUBROUTINE my25_prestep_tile
END MODULE my25_prestep_mod