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C $Header: /u/gcmpack/MITgcm/model/src/adams_bashforth3.F,v 1.2 2005/11/06 22:19:08 jmc Exp $ |
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C $Name: $ |
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|
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#include "CPP_OPTIONS.h" |
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|
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CBOP |
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C !ROUTINE: ADAMS_BASHFORTH3 |
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C !INTERFACE: |
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SUBROUTINE ADAMS_BASHFORTH3( |
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I bi, bj, kArg, |
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U gTracer, gTrNm, |
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I startAB, myIter, myThid ) |
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C !DESCRIPTION: \bv |
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C *==========================================================* |
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C | S/R ADAMS_BASHFORTH3 |
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C | o Extrapolate forward in time using third order |
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C | Adams-Bashforth method. |
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C *==========================================================* |
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C | Either apply to tendency (kArg>0) at level k=kArg, |
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C | or apply to state variable (kArg=0) for all levels |
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C *==========================================================* |
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C \ev |
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C Extrapolate forward in time using 2 A.B. parameters (alpha,beta), |
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C either tendency gX : |
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C \begin{equation*} |
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C gX^{n+1/2} = (1 + \alpha + \beta) gX^{n} |
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C - (\alpha + 2 \beta) gX^{n-1} |
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C + \beta gX^{n-2} |
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C \end{equation*} |
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C or state variable X : |
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C \begin{equation*} |
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C X^{n+1/2} = (1 + \alpha + \beta) X^{n} |
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C - (\alpha + 2 \beta) X^{n-1} |
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C + \beta X^{n-2} |
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C \end{equation*} |
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C with: |
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C (alpha,beta)=(1/2,5/12) : AB-3, stable until CFL = 0.724 |
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C (note: beta=0.281105 give the Max stability: 0.78616) |
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C (alpha,beta)=(1/2+abEps,0) : return to previous quasi AB-2. |
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C (alpha,beta)=(0,0) : 1rst.O forward time stepping |
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|
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C !USES: |
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IMPLICIT NONE |
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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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|
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C !INPUT/OUTPUT PARAMETERS: |
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C == Routine Arguments == |
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C bi,bj :: Tile indices |
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C kArg :: if >0: apply AB on tendency at level k=kArg |
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C :: if =0: apply AB on state variable and process all levels |
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C gTracer :: (kArg>0) Tendency at current time ( units of quantity/sec ) |
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C :: (kArg=0) state variable at current time |
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C gTrNm :: (kArg>0) Tendencies at previous times ( units of quantity/sec ) |
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C :: (kArg=0) state variable at previous times |
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C startAB :: number of previous time level available to start/restart AB |
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C myIter :: Current time step number |
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C myThid :: my Thread number Id |
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INTEGER bi,bj,kArg |
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_RL gTracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy) |
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_RL gTrNm (1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr,nSx,nSy,2) |
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INTEGER startAB |
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INTEGER myIter, myThid |
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|
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#ifdef ALLOW_ADAMSBASHFORTH_3 |
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C !LOCAL VARIABLES: |
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C == Local variables == |
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C k :: level index |
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C i,j :: Loop counters |
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C m1,m2 :: indices for the 2 previous time-step Tendency |
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C ab1,ab2,ab3 :: Adams bashforth extrapolation weights. |
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INTEGER i,j, k, m1,m2 |
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_RL ab0, ab1, ab2 |
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_RL gTrtmp |
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CEOP |
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|
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m1 = 1 + mod(myIter+1,2) |
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m2 = 1 + mod( myIter ,2) |
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|
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C Adams-Bashforth timestepping weights |
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IF ( myIter.EQ.nIter0 .AND. startAB.EQ.0 ) THEN |
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ab0 = 1. _d 0 |
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ab1 = 0. _d 0 |
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ab2 = 0. _d 0 |
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ELSEIF ( (myIter.EQ.nIter0 .AND. startAB.EQ.1) |
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& .OR. (myIter.EQ.1+nIter0 .AND. startAB.EQ.0) ) THEN |
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ab0 = 1. _d 0 + alph_AB |
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ab1 = -alph_AB |
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ab2 = 0. _d 0 |
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ELSE |
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ab0 = 1. _d 0 + alph_AB + beta_AB |
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ab1 = -alph_AB - 2.*beta_AB |
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ab2 = beta_AB |
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ENDIF |
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|
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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|
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IF ( kArg.EQ.0 ) THEN |
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C- Extrapolate forward in time the state variable, with AB weights: |
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DO k=1,Nr |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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gTrtmp = ab0*gTracer(i,j,k,bi,bj) |
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& + ab1*gTrNm(i,j,k,bi,bj,m1) |
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& + ab2*gTrNm(i,j,k,bi,bj,m2) |
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gTrNm(i,j,k,bi,bj,m2) = gTracer(i,j,k,bi,bj) |
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gTracer(i,j,k,bi,bj) = gTrtmp |
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ENDDO |
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ENDDO |
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ENDDO |
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ELSE |
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C- Extrapolate forward in time the tendency, with AB weights: |
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k = kArg |
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DO j=1-Oly,sNy+Oly |
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DO i=1-Olx,sNx+Olx |
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gTrtmp = ab0*gTracer(i,j,k,bi,bj) |
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& + ab1*gTrNm(i,j,k,bi,bj,m1) |
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& + ab2*gTrNm(i,j,k,bi,bj,m2) |
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gTrNm(i,j,k,bi,bj,m2) = gTracer(i,j,k,bi,bj) |
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gTracer(i,j,k,bi,bj) = gTrtmp |
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ENDDO |
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ENDDO |
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C--- |
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ENDIF |
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|
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#endif /* ALLOW_ADAMSBASHFORTH_3 */ |
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|
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RETURN |
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END |
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