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C $Header: /u/gcmpack/MITgcm/pkg/seaice/seaice_calc_lhs.F,v 1.11 2015/12/16 12:16:08 mlosch Exp $ |
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C $Name: $ |
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|
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#include "SEAICE_OPTIONS.h" |
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#ifdef ALLOW_AUTODIFF |
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# include "AUTODIFF_OPTIONS.h" |
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#endif |
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|
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CBOP |
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C !ROUTINE: SEAICE_CALC_LHS |
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C !INTERFACE: |
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SUBROUTINE SEAICE_CALC_LHS( |
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I uIceLoc, vIceLoc, |
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O uIceLHS, vIceLHS, |
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I newtonIter, myTime, myIter, myThid ) |
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|
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | SUBROUTINE SEAICE_CALC_LHS |
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C | o Left-hand side of momentum equations, i.e. all terms |
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C | that depend on the ice velocities of the current |
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C | iterate of the Newton-Krylov iteration |
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C | |
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C | o The scheme is backward Euler in time, i.e. the |
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C | rhs-vector contains only terms that are independent |
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C | of u/vIce, except for the time derivative part |
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C | mass*(u/vIce-u/vIceNm1)/deltaT |
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C | o Left-hand side contributions |
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C | + mass*(u/vIce)/deltaT |
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C | + Cdrag*(uIce*cosWat - vIce*sinWat) |
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C | /(vIce*cosWat + uIce*sinWat) |
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C | - mass*f*vIce/+mass*f*uIce |
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C | - dsigma/dx / -dsigma/dy, eta and zeta are |
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C | computed only once per Newton iterate |
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C *==========================================================* |
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C | written by Martin Losch, Oct 2012 |
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C *==========================================================* |
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C \ev |
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|
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C !USES: |
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IMPLICIT NONE |
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|
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C === Global variables === |
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#include "SIZE.h" |
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#include "EEPARAMS.h" |
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#include "PARAMS.h" |
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#include "GRID.h" |
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#include "SEAICE_SIZE.h" |
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#include "SEAICE_PARAMS.h" |
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#include "SEAICE.h" |
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|
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#ifdef ALLOW_AUTODIFF_TAMC |
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# include "tamc.h" |
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#endif |
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|
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C !INPUT/OUTPUT PARAMETERS: |
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C === Routine arguments === |
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C myTime :: Simulation time |
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C myIter :: Simulation timestep number |
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C myThid :: my Thread Id. number |
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C newtonIter :: current iterate of Newton iteration |
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_RL myTime |
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INTEGER myIter |
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INTEGER myThid |
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INTEGER newtonIter |
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C u/vIceLoc :: local copies of the current ice velocity |
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_RL uIceLoc(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL vIceLoc(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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C u/vIceLHS :: LHS of momentum equations |
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_RL uIceLHS(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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_RL vIceLHS(1-OLx:sNx+OLx,1-OLy:sNy+OLy,nSx,nSy) |
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|
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#ifdef SEAICE_ALLOW_JFNK |
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C i,j,bi,bj,k :: loop indices |
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INTEGER i,j,bi,bj |
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INTEGER k |
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_RS SINWAT |
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_RL COSWAT, recip_deltaT, eplus, eminus |
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C backward difference extrapolation factor |
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_RL bdfAlpha |
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C components of symmetric stress tensor |
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_RL sig11(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL sig22(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL sig12(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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C fractional area at velocity points |
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_RL areaW(1:sNx,1:sNy) |
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_RL areaS(1:sNx,1:sNy) |
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CEOP |
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|
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k=1 |
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recip_deltaT = 1. _d 0 / SEAICE_deltaTdyn |
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C-- introduce turning angles |
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SINWAT=SIN(SEAICE_waterTurnAngle*deg2rad) |
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COSWAT=COS(SEAICE_waterTurnAngle*deg2rad) |
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C backward difference extrapolation factor |
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bdfAlpha = 1. _d 0 |
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IF ( SEAICEuseBDF2 ) THEN |
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IF ( myIter.EQ.nIter0 .AND. SEAICEmomStartBDF.EQ.0 ) THEN |
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bdfAlpha = 1. _d 0 |
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ELSE |
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bdfAlpha = 1.5 _d 0 |
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ENDIF |
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ENDIF |
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|
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C initialise fractional areas at velocity points |
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DO J=1,sNy |
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DO I=1,sNx |
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areaW(I,J) = 1. _d 0 |
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areaS(I,J) = 1. _d 0 |
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ENDDO |
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ENDDO |
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|
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DO bj=myByLo(myThid),myByHi(myThid) |
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DO bi=myBxLo(myThid),myBxHi(myThid) |
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C compute components of stress tensor from current velocity field |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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sig11(I,J) = 0. _d 0 |
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sig22(I,J) = 0. _d 0 |
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sig12(I,J) = 0. _d 0 |
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ENDDO |
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ENDDO |
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|
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DO j=0,sNy |
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DO i=0,sNx |
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eplus = e11(I,J,bi,bj) + e22(I,J,bi,bj) |
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eminus= e11(I,J,bi,bj) - e22(I,J,bi,bj) |
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sig11(I,J) = zeta(I,J,bi,bj)*eplus + eta(I,J,bi,bj)*eminus |
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& - 0.5 _d 0 * PRESS(I,J,bi,bj) |
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sig22(I,J) = zeta(I,J,bi,bj)*eplus - eta(I,J,bi,bj)*eminus |
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& - 0.5 _d 0 * PRESS(I,J,bi,bj) |
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ENDDO |
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ENDDO |
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|
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DO j=1,sNy+1 |
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DO i=1,sNx+1 |
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sig12(I,J) = 2. _d 0 * e12(I,J,bi,bj) * etaZ(I,J,bi,bj) |
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ENDDO |
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ENDDO |
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C |
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C compute divergence of stress tensor |
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C |
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DO J=1,sNy |
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DO I=1,sNx |
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stressDivergenceX(I,J,bi,bj) = |
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& ( sig11(I ,J ) * _dyF(I ,J,bi,bj) |
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& - sig11(I-1,J ) * _dyF(I-1,J,bi,bj) |
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& + sig12(I ,J+1) * _dxV(I,J+1,bi,bj) |
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& - sig12(I ,J ) * _dxV(I,J ,bi,bj) |
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& ) * recip_rAw(I,J,bi,bj) |
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stressDivergenceY(I,J,bi,bj) = |
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& ( sig22(I ,J ) * _dxF(I,J ,bi,bj) |
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& - sig22(I ,J-1) * _dxF(I,J-1,bi,bj) |
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& + sig12(I+1,J ) * _dyU(I+1,J,bi,bj) |
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& - sig12(I ,J ) * _dyU(I ,J,bi,bj) |
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& ) * recip_rAs(I,J,bi,bj) |
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ENDDO |
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ENDDO |
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C compute lhs side of momentum equations |
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IF ( SEAICEscaleSurfStress ) THEN |
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DO J=1,sNy |
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DO I=1,sNx |
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areaW(I,J) = 0.5 _d 0*(AREA(I,J,bi,bj)+AREA(I-1,J,bi,bj)) |
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areaS(I,J) = 0.5 _d 0*(AREA(I,J,bi,bj)+AREA(I,J-1,bi,bj)) |
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ENDDO |
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ENDDO |
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ENDIF |
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DO J=1,sNy |
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DO I=1,sNx |
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C mass*(uIce)/deltaT - dsigma/dx |
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uIceLHS(I,J,bi,bj) = |
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& bdfAlpha*seaiceMassU(I,J,bi,bj)*recip_deltaT |
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& *uIceLoc(I,J,bi,bj) - stressDivergenceX(I,J,bi,bj) |
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C mass*(vIce)/deltaT - dsigma/dy |
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vIceLHS(I,J,bi,bj) = |
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& bdfAlpha*seaiceMassV(I,J,bi,bj)*recip_deltaT |
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& *vIceLoc(I,J,bi,bj) - stressDivergenceY(I,J,bi,bj) |
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C coriols terms: - mass*f*vIce |
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uIceLHS(I,J,bi,bj) = uIceLHS(I,J,bi,bj) - 0.5 _d 0*( |
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& seaiceMassC(I ,J,bi,bj) * _fCori(I ,J,bi,bj) |
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& * 0.5 _d 0*( vIceLoc(I ,J,bi,bj)+vIceLoc(I ,J+1,bi,bj) ) |
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& + seaiceMassC(I-1,J,bi,bj) * _fCori(I-1,J,bi,bj) |
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& * 0.5 _d 0*( vIceLoc(I-1,J,bi,bj)+vIceLoc(I-1,J+1,bi,bj) ) |
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& ) |
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C + mass*f*uIce |
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vIceLHS(I,J,bi,bj) = vIceLHS(I,J,bi,bj) + 0.5 _d 0*( |
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& seaiceMassC(I,J ,bi,bj) * _fCori(I,J ,bi,bj) |
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& * 0.5 _d 0*( uIceLoc(I,J ,bi,bj)+uIceLoc(I+1, J,bi,bj) ) |
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& + seaiceMassC(I,J-1,bi,bj) * _fCori(I,J-1,bi,bj) |
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& * 0.5 _d 0*( uIceLoc(I,J-1,bi,bj)+uIceLoc(I+1,J-1,bi,bj) ) |
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& ) |
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C ocean-ice drag terms: + Cdrag*(uIce*cosWat - vIce*sinWat) |
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uIceLHS(I,J,bi,bj) = uIceLHS(I,J,bi,bj) + ( |
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& 0.5 _d 0 * ( DWATN(I,J,bi,bj)+DWATN(I-1,J,bi,bj) ) * |
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& COSWAT * uIceLoc(I,J,bi,bj) |
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& - SIGN(SINWAT, _fCori(I,J,bi,bj))* 0.5 _d 0 * |
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& ( DWATN(I ,J,bi,bj) * 0.5 _d 0 * |
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& (vIceLoc(I ,J,bi,bj)+vIceLoc(I ,J+1,bi,bj)) |
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& + DWATN(I-1,J,bi,bj) * 0.5 _d 0 * |
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& (vIceLoc(I-1,J,bi,bj)+vIceLoc(I-1,J+1,bi,bj)) |
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& ) ) * areaW(I,J) |
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C + Cdrag*(vIce*cosWat + uIce*sinWat) |
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vIceLHS(I,J,bi,bj) = vIceLHS(I,J,bi,bj) + ( |
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& 0.5 _d 0 * ( DWATN(I,J,bi,bj)+DWATN(I,J-1,bi,bj) ) * |
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& COSWAT * vIceLoc(I,J,bi,bj) |
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& + SIGN(SINWAT, _fCori(I,J,bi,bj)) * 0.5 _d 0 * |
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& ( DWATN(I,J ,bi,bj) * 0.5 _d 0 * |
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& (uIceLoc(I,J ,bi,bj)+uIceLoc(I+1,J ,bi,bj)) |
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& + DWATN(I,J-1,bi,bj) * 0.5 _d 0 * |
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& (uIceLoc(I,J-1,bi,bj)+uIceLoc(I+1,J-1,bi,bj)) |
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& ) ) * areaS(I,J) |
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C apply masks for interior (important when we have open boundaries) |
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uIceLHS(I,J,bi,bj) = uIceLHS(I,J,bi,bj)*maskinW(I,J,bi,bj) |
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vIceLHS(I,J,bi,bj) = vIceLHS(I,J,bi,bj)*maskinS(I,J,bi,bj) |
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ENDDO |
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ENDDO |
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ENDDO |
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ENDDO |
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|
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#endif /* SEAICE_ALLOW_JFNK */ |
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|
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RETURN |
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END |
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