#undef NEUMANN SUBROUTINE prsgrd (ng, tile) ! !svn $Id: prsgrd42.h 889 2018-02-10 03:32:52Z arango $ !*********************************************************************** ! Copyright (c) 2002-2019 The ROMS/TOMS Group ! ! Licensed under a MIT/X style license ! ! See License_ROMS.txt Hernan G. Arango ! !****************************************** Alexander F. Shchepetkin *** ! ! ! This subroutine evaluates the baroclinic, hydrostatic pressure ! ! gradient term using a finite-volume pressure Jacobian scheme. ! ! The scheme is based on local, conservative, limited-oscillation ! ! vertical quartic polynomial reconstruction of density field and ! ! subsequent projection fits of the derivatives of density into ! ! isosurface of vertical coordinate. The monotonicity constraint ! ! uses a PPM-style limitting algorithm. ! ! ! ! The pressure gradient terms (m4/s2) are loaded into right-hand- ! ! side arrays "ru" and "rv". ! ! ! ! Reference: ! ! ! ! Shchepetkin A.F and J.C. McWilliams, 2003: A method for ! ! computing horizontal pressure gradient force in an ocean ! ! model with non-aligned vertical coordinate, JGR, 108, ! ! 1-34. ! ! ! !*********************************************************************** ! USE mod_param #ifdef DIAGNOSTICS USE mod_diags #endif #ifdef ATM_PRESS USE mod_forces #endif USE mod_grid USE mod_ocean USE mod_stepping ! ! Imported variable declarations. ! integer, intent(in) :: ng, tile ! ! Local variable declarations. ! #include "tile.h" ! #ifdef PROFILE CALL wclock_on (ng, iNLM, 23, __LINE__, __FILE__) #endif CALL prsgrd_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs(ng), & #ifdef MASKING & GRID(ng) % umask, & & GRID(ng) % vmask, & #endif #ifdef WET_DRY & GRID(ng)%umask_wet, & & GRID(ng)%vmask_wet, & #endif & GRID(ng) % Hz, & & GRID(ng) % om_v, & & GRID(ng) % on_u, & & GRID(ng) % z_w, & & OCEAN(ng) % rho, & #ifdef WEC_VF & OCEAN(ng) % zetat, & #endif #ifdef ATM_PRESS & FORCES(ng) % Pair, & #endif #ifdef DIAGNOSTICS_UV & DIAGS(ng) % DiaRU, & & DIAGS(ng) % DiaRV, & #endif & OCEAN(ng) % ru, & & OCEAN(ng) % rv) #ifdef PROFILE CALL wclock_off (ng, iNLM, 23, __LINE__, __FILE__) #endif RETURN END SUBROUTINE prsgrd ! !*********************************************************************** SUBROUTINE prsgrd_tile (ng, tile, & & LBi, UBi, LBj, UBj, & & IminS, ImaxS, JminS, JmaxS, & & nrhs, & #ifdef MASKING & umask, vmask, & #endif #ifdef WET_DRY & umask_wet, vmask_wet, & #endif & Hz, om_v, on_u, z_w, & & rho, & #ifdef WEC_VF & zetat, & #endif #ifdef ATM_PRESS & Pair, & #endif #ifdef DIAGNOSTICS_UV & DiaRU, DiaRV, & #endif & ru, rv) !*********************************************************************** ! USE mod_param USE mod_scalars ! ! 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) :: nrhs ! #ifdef ASSUMED_SHAPE # ifdef MASKING real(r8), intent(in) :: umask(LBi:,LBj:) real(r8), intent(in) :: vmask(LBi:,LBj:) # endif # ifdef WET_DRY real(r8), intent(in) :: umask_wet(LBi:,LBj:) real(r8), intent(in) :: vmask_wet(LBi:,LBj:) # endif real(r8), intent(in) :: Hz(LBi:,LBj:,:) real(r8), intent(in) :: om_v(LBi:,LBj:) real(r8), intent(in) :: on_u(LBi:,LBj:) real(r8), intent(in) :: z_w(LBi:,LBj:,0:) real(r8), intent(in) :: rho(LBi:,LBj:,:) # ifdef WEC_VF real(r8), intent(in) :: zetat(LBi:,LBj:) # endif # ifdef ATM_PRESS real(r8), intent(in) :: Pair(LBi:,LBj:) # endif # ifdef DIAGNOSTICS_UV real(r8), intent(inout) :: DiaRU(LBi:,LBj:,:,:,:) real(r8), intent(inout) :: DiaRV(LBi:,LBj:,:,:,:) # endif real(r8), intent(inout) :: ru(LBi:,LBj:,0:,:) real(r8), intent(inout) :: rv(LBi:,LBj:,0:,:) #else # ifdef MASKING real(r8), intent(in) :: umask(LBi:UBi,LBj:UBj) real(r8), intent(in) :: vmask(LBi:UBi,LBj:UBj) # endif # ifdef WET_DRY real(r8), intent(in) :: umask_wet(LBi:UBi,LBj:UBj) real(r8), intent(in) :: vmask_wet(LBi:UBi,LBj:UBj) # endif real(r8), intent(in) :: Hz(LBi:UBi,LBj:UBj,N(ng)) real(r8), intent(in) :: om_v(LBi:UBi,LBj:UBj) real(r8), intent(in) :: on_u(LBi:UBi,LBj:UBj) real(r8), intent(in) :: z_w(LBi:UBi,LBj:UBj,0:N(ng)) real(r8), intent(in) :: rho(LBi:UBi,LBj:UBj,N(ng)) # ifdef WEC_VF real(r8), intent(in) :: zetat(LBi:UBi,LBj:UBj) # endif # ifdef ATM_PRESS real(r8), intent(in) :: Pair(LBi:UBi,LBj:UBj) # endif # ifdef DIAGNOSTICS_UV real(r8), intent(inout) :: DiaRU(LBi:UBi,LBj:UBj,N(ng),2,NDrhs) real(r8), intent(inout) :: DiaRV(LBi:UBi,LBj:UBj,N(ng),2,NDrhs) # endif real(r8), intent(inout) :: ru(LBi:UBi,LBj:UBj,0:N(ng),2) real(r8), intent(inout) :: rv(LBi:UBi,LBj:UBj,0:N(ng),2) #endif ! ! Local variable declarations. ! integer :: i, j, k real(r8), parameter :: eps = 1.0E-8_r8 real(r8) :: cff, cff1, cff2, cffL, cffR real(r8) :: deltaL, deltaR, dh, dP, rr #ifdef ATM_PRESS real(r8) :: OneAtm, fac #endif real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: FX real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: P real(r8), dimension(IminS:ImaxS,JminS:JmaxS,0:N(ng)) :: r real(r8), dimension(IminS:ImaxS,0:N(ng)) :: FC real(r8), dimension(IminS:ImaxS,0:N(ng)) :: aL real(r8), dimension(IminS:ImaxS,0:N(ng)) :: aR real(r8), dimension(IminS:ImaxS,0:N(ng)) :: dL real(r8), dimension(IminS:ImaxS,0:N(ng)) :: dR #include "set_bounds.h" ! !--------------------------------------------------------------------- ! Finite-volume pressure gradient force algorithm. !--------------------------------------------------------------------- ! #ifdef ATM_PRESS OneAtm=1013.25_r8 ! 1 atm = 1013.25 mb fac=100.0_r8/g #endif cff2=1.0_r8/6.0_r8 DO j=JstrV-2,Jend+1 DO k=N(ng)-1,1,-1 DO i=IstrU-2,Iend+1 FC(i,k)=(rho(i,j,k+1)-rho(i,j,k))/(Hz(i,j,k+1)+Hz(i,j,k)) END DO END DO ! ! Parabolic WENO reconstruction of density field. Compute left and ! right side limits aL and aR for the density assuming monotonized ! parabolic distributions within each grid box. Also compute dL and ! dR which are used as a measure of quadratic variation during ! subsquent WENO reconciliation of side limits. ! DO k=2,N(ng)-1 DO i=IstrU-2,Iend+1 deltaR=Hz(i,j,k)*FC(i,k) deltaL=Hz(i,j,k)*FC(i,k-1) IF ((deltaR*deltaL).lt.0.0_r8) THEN deltaR=0.0_r8 deltaL=0.0_r8 END IF cff=Hz(i,j,k-1)+2.0_r8*Hz(i,j,k)+Hz(i,j,k+1) cffR=cff*FC(i,k) cffL=cff*FC(i,k-1) IF (ABS(deltaR).gt.ABS(cffL)) deltaR=cffL IF (ABS(deltaL).gt.ABS(cffR)) deltaL=cffR cff=(deltaR-deltaL)/(Hz(i,j,k-1)+Hz(i,j,k)+Hz(i,j,k+1)) deltaR=deltaR-cff*Hz(i,j,k+1) deltaL=deltaL+cff*Hz(i,j,k-1) aR(i,k)=rho(i,j,k)+deltaR aL(i,k)=rho(i,j,k)-deltaL dR(i,k)=(2.0_r8*deltaR-deltaL)**2 dL(i,k)=(2.0_r8*deltaL-deltaR)**2 END DO END DO ! DO i=IstrU-2,Iend+1 aL(i,N(ng))=aR(i,N(ng)-1) aR(i,N(ng))=2.0_r8*rho(i,j,N(ng))-aL(i,N(ng)) dR(i,N(ng))=(2.0_r8*aR(i,N(ng))+aL(i,N(ng))- & & 3.0_r8*rho(i,j,N(ng)))**2 dL(i,N(ng))=(3.0_r8*rho(i,j,N(ng))- & & 2.0_r8*aL(i,N(ng))-aR(i,N(ng)))**2 aR(i,1)=aL(i,2) aL(i,1)=2.0_r8*rho(i,j,1)-aR(i,1) dR(i,1)=(2.0_r8*aR(i,1)+aL(i,1)-3.0_r8*rho(i,j,1))**2 dL(i,1)=(3.0_r8*rho(i,j,1)-2.0_r8*aL(i,1)-aR(i,1))**2 END DO ! DO k=1,N(ng)-1 DO i=IstrU-2,Iend+1 deltaL=MAX(dL(i,k ),eps) deltaR=MAX(dR(i,k+1),eps) r(i,j,k)=(deltaR*aR(i,k)+deltaL*aL(i,k+1))/ & & (deltaR+deltaL) END DO END DO ! DO i=IstrU-2,Iend+1 #ifdef NEUMANN r(i,j,N(ng))=1.5_r8*rho(i,j,N(ng))-0.5_r8*r(i,j,N(ng)-1) r(i,j,0)=1.5_r8*rho(i,j,1)-0.5_r8*r(i,j,1 ) #else r(i,j,N(ng))=2.0_r8*rho(i,j,N(ng))-r(i,j,N(ng)-1) r(i,j,0)=2.0_r8*rho(i,j,1)-r(i,j,1 ) #endif END DO ! ! Compute pressure (P) and lateral pressure force (FX). Initialize ! pressure at the free-surface as zero ! DO i=IstrU-2,Iend+1 P(i,j,N(ng))=0.0_r8 #ifdef WEC_VF P(i,j,N(ng))=P(i,j,N(ng))+zetat(i,j) #endif #ifdef ATM_PRESS P(i,j,N(ng))=P(i,j,N(ng))+fac*(Pair(i,j)-OneAtm) #endif END DO DO k=N(ng),1,-1 DO i=IstrU-2,Iend+1 P(i,j,k-1)=P(i,j,k)+Hz(i,j,k)*rho(i,j,k) deltaR=r(i,j,k)-rho(i,j,k) deltaL=rho(i,j,k)-r(i,j,k-1) IF ((deltaR*deltaL).lt.0.0_r8) THEN rr=0.0_r8 ELSE IF (ABS(deltaR).gt.(2.0_r8*ABS(deltaL))) THEN rr=3.0_r8*deltaL ELSE IF (ABS(deltaL).gt.(2.0_r8*ABS(deltaR))) THEN rr=3.0_r8*deltaR ELSE rr=deltaR+deltaL END IF FX(i,j,k)=0.5_r8*Hz(i,j,k)* & & (P(i,j,k)+P(i,j,k-1)+cff2*rr*Hz(i,j,k)) END DO END DO ! ! Compute net pressure gradient forces in the XI-directions. ! Set pressure at free-surface as zero. ! IF ((j.ge.Jstr).and.(j.le.Jend)) THEN DO i=IstrU-1,Iend+1 FC(i,N(ng))=0.0_r8 END DO DO k=N(ng),1,-1 DO i=IstrU-1,Iend+1 dP=P(i-1,j,k-1)-P(i,j,k-1) dh=z_w(i,j,k-1)-z_w(i-1,j,k-1) deltaR=dh*r(i,j,k-1)-dP deltaL=dP-dh*r(i-1,j,k-1) IF ((deltaR*deltaL).lt.0.0_r8) THEN rr=0.0_r8 ELSE IF (ABS(deltaR).gt.(2.0_r8*ABS(deltaL))) THEN rr=3.0_r8*deltaL ELSE IF (ABS(deltaL).gt.(2.0_r8*ABS(deltaR))) THEN rr=3.0_r8*deltaR ELSE rr=deltaR+deltaL END IF FC(i,k-1)=0.5_r8*dh*(P(i,j,k-1)+P(i-1,j,k-1)+cff2*rr) ru(i,j,k,nrhs)=2.0_r8*(FX(i-1,j,k)-FX(i,j,k)+ & & FC(i,k)-FC(i,k-1))/ & & (Hz(i-1,j,k)+Hz(i,j,k)) #ifdef MASKING ru(i,j,k,nrhs)=ru(i,j,k,nrhs)*umask(i,j) #endif #ifdef WET_DRY ru(i,j,k,nrhs)=ru(i,j,k,nrhs)*umask_wet(i,j) #endif END DO END DO END IF ! ! Compute net pressure gradient forces in the ETA-directions. ! Set pressure at free-surface as zero. ! IF (j.ge.JstrV-1) THEN DO i=Istr,Iend FC(i,N(ng))=0.0_r8 END DO DO k=N(ng),1,-1 DO i=Istr,Iend dP=P(i,j-1,k-1)-P(i,j,k-1) dh=z_w(i,j,k-1)-z_w(i,j-1,k-1) deltaR=dh*r(i,j,k-1)-dP deltaL=dP-dh*r(i,j-1,k-1) IF ((deltaR*deltaL).lt.0.0_r8) THEN rr=0.0_r8 ELSE IF (ABS(deltaR).gt.(2.0_r8*ABS(deltaL))) THEN rr=3.0_r8*deltaL ELSE IF (ABS(deltaL).gt.(2.0_r8*ABS(deltaR))) THEN rr=3.0_r8*deltaR ELSE rr=deltaR+deltaL END IF FC(i,k-1)=0.5_r8*dh*(P(i,j,k-1)+P(i,j-1,k-1)+cff2*rr) rv(i,j,k,nrhs)=2.0_r8*(FX(i,j-1,k)-FX(i,j,k)+ & & FC(i,k)-FC(i,k-1))/ & & (Hz(i,j-1,k)+Hz(i,j,k)) #ifdef MASKING rv(i,j,k,nrhs)=rv(i,j,k,nrhs)*vmask(i,j) #endif #ifdef WET_DRY rv(i,j,k,nrhs)=rv(i,j,k,nrhs)*vmask_wet(i,j) #endif END DO END DO END IF END DO ! rr=g/(24.0_r8*rho0) cff=0.5_r8*g cff1=0.5_r8*g/rho0 DO j=Jstr,Jend DO k=N(ng)-1,1,-1 DO i=IstrU,Iend dh=rr*(z_w(i,j,k)-z_w(i-1,j,k)) FC(i,k)=MAX(dh,0.0_r8)* & & (ru(i,j,k+1,nrhs)+ru(i+1,j,k ,nrhs)- & & ru(i,j,k ,nrhs)-ru(i-1,j,k+1,nrhs))+ & & MIN(dh,0.0_r8)* & & (ru(i,j,k ,nrhs)+ru(i+1,j,k+1,nrhs)- & & ru(i,j,k+1,nrhs)-ru(i-1,j,k ,nrhs)) END DO END DO DO i=IstrU,Iend FC(i,N(ng))=0.0_r8 dh=rr*(z_w(i,j,0)-z_w(i-1,j,0)) FC(i,0)=MAX(dh,0.0_r8)* & & (ru(i ,j,1,nrhs)-ru(i-1,j,1,nrhs))+ & & MIN(dh,0.0_r8)* & & (ru(i+1,j,1,nrhs)-ru(i ,j,1,nrhs)) END DO DO k=1,N(ng) DO i=IstrU,Iend ru(i,j,k,nrhs)=(cff*(z_w(i-1,j,N(ng))-z_w(i,j,N(ng)))+ & & cff1*ru(i,j,k,nrhs))* & & (Hz(i-1,j,k)+Hz(i,j,k))*on_u(i,j)+ & & (FC(i,k)-FC(i,k-1))*on_u(i,j) #ifdef DIAGNOSTICS_UV DiaRU(i,j,k,nrhs,M3pgrd)=ru(i,j,k,nrhs) #endif END DO END DO END DO ! DO j=JstrV,Jend DO k=N(ng)-1,1,-1 DO i=Istr,Iend dh=rr*(z_w(i,j,k)-z_w(i,j-1,k)) FX(i,j,k)=MAX(dh,0.0_r8)* & & (rv(i,j,k+1,nrhs)+rv(i+1,j ,k ,nrhs)- & & rv(i,j,k ,nrhs)-rv(i ,j-1,k+1,nrhs))+ & & MIN(dh,0.0_r8)* & & (rv(i,j,k ,nrhs)+rv(i+1,j ,k+1,nrhs)- & & rv(i,j,k+1,nrhs)-rv(i ,j-1,k ,nrhs)) END DO END DO DO i=Istr,Iend FX(i,j,N(ng))=0.0_r8 dh=rr*(z_w(i,j,0)-z_w(i,j-1,0)) FX(i,j,0)=MAX(dh,0.0_r8)* & & (rv(i ,j,1,nrhs)-rv(i,j-1,1,nrhs))+ & & MIN(dh,0.0_r8)* & & (rv(i+1,j,1,nrhs)-rv(i,j ,1,nrhs)) END DO END DO DO j=JstrV,Jend DO k=1,N(ng) DO i=Istr,Iend rv(i,j,k,nrhs)=(cff*(z_w(i,j-1,N(ng))-z_w(i,j,N(ng)))+ & & cff1*rv(i,j,k,nrhs))* & & (Hz(i,j-1,k)+Hz(i,j,k))*om_v(i,j)+ & & (FX(i,j,k)-FX(i,j,k-1))*om_v(i,j) #ifdef DIAGNOSTICS_UV DiaRV(i,j,k,nrhs,M3pgrd)=rv(i,j,k,nrhs) #endif END DO END DO END DO RETURN END SUBROUTINE prsgrd_tile