C $Header: /u/gcmpack/MITgcm/pkg/seaice/seaice_calc_lhs.F,v 1.16 2017/05/23 16:22:45 mlosch Exp $
C $Name: $
#include "SEAICE_OPTIONS.h"
#ifdef ALLOW_AUTODIFF
# include "AUTODIFF_OPTIONS.h"
#endif
CBOP
C !ROUTINE: SEAICE_CALC_LHS
C !INTERFACE:
SUBROUTINE SEAICE_CALC_LHS(
I uIceLoc, vIceLoc,
O uIceLHS, vIceLHS,
I newtonIter, myTime, myIter, myThid )
C !DESCRIPTION: \bv
C *==========================================================*
C | SUBROUTINE SEAICE_CALC_LHS
C | o Left-hand side of momentum equations, i.e. all terms
C | that depend on the ice velocities of the current
C | iterate of the Newton-Krylov iteration
C |
C | o The scheme is backward Euler in time, i.e. the
C | rhs-vector contains only terms that are independent
C | of u/vIce, except for the time derivative part
C | mass*(u/vIce-u/vIceNm1)/deltaT
C | o Left-hand side contributions
C | + mass*(u/vIce)/deltaT
C | + Cdrag*(uIce*cosWat - vIce*sinWat)
C | /(vIce*cosWat + uIce*sinWat)
C | - mass*f*vIce/+mass*f*uIce
C | - dsigma/dx / -dsigma/dy, eta and zeta are
C | computed only once per Newton iterate
C *==========================================================*
C | written by Martin Losch, Oct 2012
C *==========================================================*
C \ev
C !USES:
IMPLICIT NONE
C === Global variables ===
#include "SIZE.h"
#include "EEPARAMS.h"
#include "PARAMS.h"
#include "GRID.h"
#include "SEAICE_SIZE.h"
#include "SEAICE_PARAMS.h"
#include "SEAICE.h"
#ifdef ALLOW_AUTODIFF_TAMC
# include "tamc.h"
#endif
C !INPUT/OUTPUT PARAMETERS:
C === Routine arguments ===
C myTime :: Simulation time
C myIter :: Simulation timestep number
C myThid :: my Thread Id. number
C newtonIter :: current iterate of Newton iteration
_RL myTime
INTEGER myIter
INTEGER myThid
INTEGER newtonIter
C u/vIceLoc :: local copies of the current ice velocity
_RL uIceLoc(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
_RL vIceLoc(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
C u/vIceLHS :: LHS of momentum equations
_RL uIceLHS(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
_RL vIceLHS(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy)
#ifdef SEAICE_ALLOW_JFNK
C i,j,bi,bj,k :: loop indices
INTEGER i,j,bi,bj
INTEGER k
_RS SINWAT
_RL COSWAT, recip_deltaT, eplus, eminus
C backward difference extrapolation factor
_RL bdfAlpha
C symmetric drag coefficient
_RL dragSym(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
C fractional area at velocity points
_RL areaW(1:sNx,1:sNy)
_RL areaS(1:sNx,1:sNy)
#ifdef SEAICE_ALLOW_MOM_ADVECTION
C tendency due to advection of momentum
_RL gUmom(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL gVmom(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
#endif /* SEAICE_ALLOW_MOM_ADVECTION */
CEOP
k=1
recip_deltaT = 1. _d 0 / SEAICE_deltaTdyn
C-- introduce turning angles
SINWAT=SIN(SEAICE_waterTurnAngle*deg2rad)
COSWAT=COS(SEAICE_waterTurnAngle*deg2rad)
C backward difference extrapolation factor
bdfAlpha = 1. _d 0
IF ( SEAICEuseBDF2 ) THEN
IF ( myIter.EQ.nIter0 .AND. SEAICEmomStartBDF.EQ.0 ) THEN
bdfAlpha = 1. _d 0
ELSE
bdfAlpha = 1.5 _d 0
ENDIF
ENDIF
C initialise fractional areas at velocity points
DO J=1,sNy
DO I=1,sNx
areaW(I,J) = 1. _d 0
areaS(I,J) = 1. _d 0
ENDDO
ENDDO
DO bj=myByLo(myThid),myByHi(myThid)
DO bi=myBxLo(myThid),myBxHi(myThid)
C symmetric drag coefficient may include bottomdrag for grounded ice
DO j=1-OLy,sNy+OLy
DO i=1-OLx,sNx+OLx
dragSym(I,J) = DWATN(I,J,bi,bj)*COSWAT
#ifdef SEAICE_ALLOW_BOTTOMDRAG
& +CbotC(I,J,bi,bj)
#endif /* SEAICE_ALLOW_BOTTOMDRAG */
ENDDO
ENDDO
C
C compute components of stress tensor from current velocity field
C and compute divergence of stress tensor
C
CALL SEAICE_CALC_STRESSDIV(
I e11, e22, e12, press, zeta, eta, etaZ,
O stressDivergenceX, stressDivergenceY,
I bi, bj, myTime, myIter, myThid )
C compute lhs side of momentum equations
IF ( SEAICEscaleSurfStress ) THEN
DO J=1,sNy
DO I=1,sNx
areaW(I,J) = 0.5 _d 0*(AREA(I,J,bi,bj)+AREA(I-1,J,bi,bj))
areaS(I,J) = 0.5 _d 0*(AREA(I,J,bi,bj)+AREA(I,J-1,bi,bj))
ENDDO
ENDDO
ENDIF
DO J=1,sNy
DO I=1,sNx
C mass*(uIce)/deltaT - dsigma/dx
uIceLHS(I,J,bi,bj) =
& bdfAlpha*seaiceMassU(I,J,bi,bj)*recip_deltaT
& *uIceLoc(I,J,bi,bj) - stressDivergenceX(I,J,bi,bj)
C mass*(vIce)/deltaT - dsigma/dy
vIceLHS(I,J,bi,bj) =
& bdfAlpha*seaiceMassV(I,J,bi,bj)*recip_deltaT
& *vIceLoc(I,J,bi,bj) - stressDivergenceY(I,J,bi,bj)
C coriols terms: - mass*f*vIce
uIceLHS(I,J,bi,bj) = uIceLHS(I,J,bi,bj) - 0.5 _d 0*(
& seaiceMassC(I ,J,bi,bj) * _fCori(I ,J,bi,bj)
& * 0.5 _d 0*( vIceLoc(I ,J,bi,bj)+vIceLoc(I ,J+1,bi,bj) )
& + seaiceMassC(I-1,J,bi,bj) * _fCori(I-1,J,bi,bj)
& * 0.5 _d 0*( vIceLoc(I-1,J,bi,bj)+vIceLoc(I-1,J+1,bi,bj) )
& )
C + mass*f*uIce
vIceLHS(I,J,bi,bj) = vIceLHS(I,J,bi,bj) + 0.5 _d 0*(
& seaiceMassC(I,J ,bi,bj) * _fCori(I,J ,bi,bj)
& * 0.5 _d 0*( uIceLoc(I,J ,bi,bj)+uIceLoc(I+1, J,bi,bj) )
& + seaiceMassC(I,J-1,bi,bj) * _fCori(I,J-1,bi,bj)
& * 0.5 _d 0*( uIceLoc(I,J-1,bi,bj)+uIceLoc(I+1,J-1,bi,bj) )
& )
C ocean-ice and bottom drag terms: + (Cdrag*cosWat+Cb)*uIce - vIce*sinWat)
uIceLHS(I,J,bi,bj) = uIceLHS(I,J,bi,bj) + (
& 0.5 _d 0 * ( dragSym(I,J)+dragSym(I-1,J) )
& * uIceLoc(I,J,bi,bj)
& - SIGN(SINWAT, _fCori(I,J,bi,bj))* 0.5 _d 0 *
& ( DWATN(I ,J,bi,bj) * 0.5 _d 0 *
& (vIceLoc(I ,J,bi,bj)+vIceLoc(I ,J+1,bi,bj))
& + DWATN(I-1,J,bi,bj) * 0.5 _d 0 *
& (vIceLoc(I-1,J,bi,bj)+vIceLoc(I-1,J+1,bi,bj))
& ) ) * areaW(I,J)
C + (Cdrag*cosWat+Cb)*uIce + uIce*sinWat)
vIceLHS(I,J,bi,bj) = vIceLHS(I,J,bi,bj) + (
& 0.5 _d 0 * ( dragSym(I,J)+dragSym(I,J-1) )
& * vIceLoc(I,J,bi,bj)
& + SIGN(SINWAT, _fCori(I,J,bi,bj)) * 0.5 _d 0 *
& ( DWATN(I,J ,bi,bj) * 0.5 _d 0 *
& (uIceLoc(I,J ,bi,bj)+uIceLoc(I+1,J ,bi,bj))
& + DWATN(I,J-1,bi,bj) * 0.5 _d 0 *
& (uIceLoc(I,J-1,bi,bj)+uIceLoc(I+1,J-1,bi,bj))
& ) ) * areaS(I,J)
C apply masks for interior (important when we have open boundaries)
uIceLHS(I,J,bi,bj) = uIceLHS(I,J,bi,bj)*maskinW(I,J,bi,bj)
vIceLHS(I,J,bi,bj) = vIceLHS(I,J,bi,bj)*maskinS(I,J,bi,bj)
ENDDO
ENDDO
#ifdef SEAICE_ALLOW_MOM_ADVECTION
IF ( SEAICEmomAdvection ) THEN
DO J=1-Oly,sNy+Oly
DO I=1-Olx,sNx+Olx
gUmom(I,J) = 0. _d 0
gVmom(I,J) = 0. _d 0
ENDDO
ENDDO
CALL SEAICE_MOM_ADVECTION(
I bi,bj,1,sNx,1,sNy,
I uIceLoc, vIceLoc,
O gUmom, gVmom,
I myTime, myIter, myThid )
C Beware of sign! gU/Vmom is computed for the rhs of the equation;
C therefore, we need to substract gU/Vmom from the left hand side
DO J=1,sNy
DO I=1,sNx
uIceLHS(I,J,bi,bj) = uIceLHS(I,J,bi,bj) - gUmom(I,J)
vIceLHS(I,J,bi,bj) = vIceLHS(I,J,bi,bj) - gVmom(I,J)
ENDDO
ENDDO
ENDIF
#endif /* SEAICE_ALLOW_MOM_ADVECTION */
ENDDO
ENDDO
#endif /* SEAICE_ALLOW_JFNK */
RETURN
END