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C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_som_adv_y.F,v 1.2 2007/08/22 00:26:01 jmc Exp $ |
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C $Name: $ |
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|
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#include "GAD_OPTIONS.h" |
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|
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CBOP |
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C !ROUTINE: GAD_SOM_ADV_Y |
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|
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C !INTERFACE: ========================================================== |
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SUBROUTINE GAD_SOM_ADV_Y( |
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I bi,bj,k, limiter, |
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I deltaTloc, vTrans, |
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U sm_v, sm_o, sm_x, sm_y, sm_z, |
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U sm_xx, sm_yy, sm_zz, sm_xy, sm_xz, sm_yz, |
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O vT, |
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I myThid ) |
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|
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C !DESCRIPTION: |
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C Calculates the area integrated meridional flux due to advection |
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C of a tracer using |
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C-- |
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C Second-Order Moments Advection of tracer in Y-direction |
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C ref: M.J.Prather, 1986, JGR, 91, D6, pp 6671-6681. |
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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C The 3-D grid has dimension (Nx,Ny,Nz) with corresponding |
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C velocity field (U,V,W). Parallel subroutine calculate |
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C advection in the X- and Z- directions. |
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C The moment [Si] are as defined in the text, Sm refers to |
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C the total mass in each grid box |
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C the moments [Fi] are similarly defined and used as temporary |
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C storage for portions of the grid boxes in transit. |
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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|
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C !USES: =============================================================== |
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IMPLICIT NONE |
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#include "SIZE.h" |
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c #include "GRID.h" |
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#include "GAD.h" |
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|
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C !INPUT PARAMETERS: =================================================== |
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C bi,bj :: tile indices |
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C k :: vertical level |
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C limiter :: 0: no limiter ; 1: Prather, 1986 limiter |
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C vTrans :: zonal volume transport |
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C myThid :: my Thread Id. number |
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INTEGER bi,bj,k |
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INTEGER limiter |
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_RL deltaTloc |
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_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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c _RL tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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INTEGER myThid |
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|
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C !OUTPUT PARAMETERS: ================================================== |
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C sm_v :: volume of grid cell |
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C sm_o :: tracer content of grid cell (zero order moment) |
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C sm_x,y,z :: 1rst order moment of tracer distribution, in x,y,z direction |
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C sm_xx,yy,zz :: 2nd order moment of tracer distribution, in x,y,z direction |
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C sm_xy,xz,yz :: 2nd order moment of tracer distr., in cross direction xy,xz,yz |
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C vT :: meridional advective flux |
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_RL sm_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL sm_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL sm_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL sm_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL sm_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL sm_xx (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL sm_yy (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL sm_zz (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL sm_xy (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL sm_xz (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL sm_yz (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL vT (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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|
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#ifdef GAD_ALLOW_SOM_ADVECT |
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C !LOCAL VARIABLES: ==================================================== |
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C i,j :: loop indices |
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C vLoc :: volume transported (per time step) |
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_RL two, three |
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PARAMETER( two = 2. _d 0 ) |
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PARAMETER( three = 3. _d 0 ) |
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INTEGER i,j |
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_RL recip_dT |
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_RL slpmax, s1max, s1new, s2new |
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_RL vLoc, alf1, alf1q, alpmn |
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_RL alfp, alpq, alp1, locTp |
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_RL alfn, alnq, aln1, locTn |
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_RL alp (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL aln (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fp_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fn_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fp_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fn_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fp_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fn_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fp_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fn_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fp_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fn_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fp_xx(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fn_xx(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fp_yy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fn_yy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fp_zz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fn_zz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fp_xy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fn_xy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fp_xz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fn_xz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fp_yz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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_RL fn_yz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
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CEOP |
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|
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recip_dT = 0. |
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IF ( deltaTloc.GT.0. _d 0 ) recip_dT = 1.0 _d 0 / deltaTloc |
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|
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IF ( limiter.EQ.1 ) THEN |
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DO j=1-OLy,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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C If flux-limiting transport is to be applied, place limits on |
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C appropriate moments before transport. |
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slpmax = 0. |
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IF ( sm_o(i,j).GT.0. ) slpmax = sm_o(i,j) |
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s1max = slpmax*1.5 _d 0 |
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s1new = MIN( s1max, MAX(-s1max,sm_y(i,j)) ) |
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s2new = MIN( (slpmax+slpmax-ABS(s1new)/three), |
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& MAX(ABS(s1new)-slpmax,sm_yy(i,j)) ) |
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sm_xy(i,j) = MIN( slpmax, MAX(-slpmax,sm_xy(i,j)) ) |
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sm_yz(i,j) = MIN( slpmax, MAX(-slpmax,sm_yz(i,j)) ) |
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sm_y (i,j) = s1new |
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sm_yy(i,j) = s2new |
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ENDDO |
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ENDDO |
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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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C--- part.1 : calculate flux for all moments |
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DO i=1-OLx,sNx+OLx |
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vT(i,1-OLy)=0. |
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ENDDO |
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DO j=1-OLy+1,sNy+OLy |
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DO i=1-OLx,sNx+OLx |
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vLoc = vTrans(i,j)*deltaTloc |
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C-- Flux from (j-1) to (j) when V>0 (i.e., take right side of box j-1) |
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fp_v (i,j) = MAX( 0. _d 0, vLoc ) |
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alp (i,j) = fp_v(i,j)/sm_v(i,j-1) |
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alpq = alp(i,j)*alp(i,j) |
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alp1 = 1. _d 0 - alp(i,j) |
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C- Create temporary moments/masses for partial boxes in transit |
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C use same indexing as velocity, "p" for positive V |
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fp_o (i,j) = alp(i,j)*( sm_o(i,j-1) + alp1*sm_y(i,j-1) |
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& + alp1*(alp1-alp(i,j))*sm_yy(i,j-1) |
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& ) |
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fp_y (i,j) = alpq *( sm_y(i,j-1) + three*alp1*sm_yy(i,j-1) ) |
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fp_yy(i,j) = alp(i,j)*alpq*sm_yy(i,j-1) |
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fp_x (i,j) = alp(i,j)*( sm_x(i,j-1) + alp1*sm_xy(i,j-1) ) |
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fp_z (i,j) = alp(i,j)*( sm_z(i,j-1) + alp1*sm_yz(i,j-1) ) |
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|
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fp_xy(i,j) = alpq *sm_xy(i,j-1) |
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fp_yz(i,j) = alpq *sm_yz(i,j-1) |
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fp_xx(i,j) = alp(i,j)*sm_xx(i,j-1) |
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fp_zz(i,j) = alp(i,j)*sm_zz(i,j-1) |
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fp_xz(i,j) = alp(i,j)*sm_xz(i,j-1) |
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C-- Flux from (j) to (j-1) when V<0 (i.e., take left side of box j) |
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fn_v (i,j) = MAX( 0. _d 0, -vLoc ) |
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aln (i,j) = fn_v(i,j)/sm_v(i, j ) |
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alnq = aln(i,j)*aln(i,j) |
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aln1 = 1. _d 0 - aln(i,j) |
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C- Create temporary moments/masses for partial boxes in transit |
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C use same indexing as velocity, "n" for negative V |
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fn_o (i,j) = aln(i,j)*( sm_o(i, j ) - aln1*sm_y(i, j ) |
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& + aln1*(aln1-aln(i,j))*sm_yy(i, j ) |
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& ) |
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fn_y (i,j) = alnq *( sm_y(i, j ) - three*aln1*sm_yy(i, j ) ) |
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fn_yy(i,j) = aln(i,j)*alnq*sm_yy(i, j ) |
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fn_x (i,j) = aln(i,j)*( sm_x(i, j ) - aln1*sm_xy(i, j ) ) |
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fn_z (i,j) = aln(i,j)*( sm_z(i, j ) - aln1*sm_yz(i, j ) ) |
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fn_xy(i,j) = alnq *sm_xy(i, j ) |
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fn_yz(i,j) = alnq *sm_yz(i, j ) |
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fn_xx(i,j) = aln(i,j)*sm_xx(i, j ) |
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fn_zz(i,j) = aln(i,j)*sm_zz(i, j ) |
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fn_xz(i,j) = aln(i,j)*sm_xz(i, j ) |
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C-- Save zero-order flux: |
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vT(i,j) = ( fp_o(i,j) - fn_o(i,j) )*recip_dT |
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ENDDO |
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ENDDO |
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|
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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C--- part.2 : re-adjust moments remaining in the box |
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C take off from grid box (j): negative V(j) and positive V(j+1) |
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DO j=1-OLy+1,sNy+OLy-1 |
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DO i=1-OLx,sNx+OLx |
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alf1 = 1. _d 0 - aln(i,j) - alp(i,j+1) |
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alf1q = alf1*alf1 |
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alpmn = alp(i,j+1) - aln(i,j) |
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sm_v (i,j) = sm_v (i,j) - fn_v (i,j) - fp_v (i,j+1) |
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sm_o (i,j) = sm_o (i,j) - fn_o (i,j) - fp_o (i,j+1) |
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sm_y (i,j) = alf1q*( sm_y(i,j) - three*alpmn*sm_yy(i,j) ) |
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sm_yy(i,j) = alf1*alf1q*sm_yy(i,j) |
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sm_xy(i,j) = alf1q*sm_xy(i,j) |
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sm_yz(i,j) = alf1q*sm_yz(i,j) |
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sm_x (i,j) = sm_x (i,j) - fn_x (i,j) - fp_x (i,j+1) |
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sm_xx(i,j) = sm_xx(i,j) - fn_xx(i,j) - fp_xx(i,j+1) |
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sm_z (i,j) = sm_z (i,j) - fn_z (i,j) - fp_z (i,j+1) |
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sm_zz(i,j) = sm_zz(i,j) - fn_zz(i,j) - fp_zz(i,j+1) |
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sm_xz(i,j) = sm_xz(i,j) - fn_xz(i,j) - fp_xz(i,j+1) |
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ENDDO |
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ENDDO |
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|
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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C--- part.3 : Put the temporary moments into appropriate neighboring boxes |
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C add into grid box (j): positive V(j) and negative V(j+1) |
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DO j=1-OLy+1,sNy+OLy-1 |
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DO i=1-OLx,sNx+OLx |
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sm_v (i,j) = sm_v (i,j) + fp_v (i,j) + fn_v (i,j+1) |
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alfp = fp_v(i, j )/sm_v(i,j) |
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alfn = fn_v(i,j+1)/sm_v(i,j) |
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alf1 = 1. _d 0 - alfp - alfn |
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alp1 = 1. _d 0 - alfp |
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aln1 = 1. _d 0 - alfn |
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alpmn = alfp - alfn |
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locTp = alfp*sm_o(i,j) - alp1*fp_o(i,j) |
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locTn = alfn*sm_o(i,j) - aln1*fn_o(i,j+1) |
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sm_yy(i,j) = alf1*alf1*sm_yy(i,j) + alfp*alfp*fp_yy(i,j) |
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& + alfn*alfn*fn_yy(i,j+1) |
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& - 5. _d 0*(-alpmn*alf1*sm_y(i,j) + alfp*alp1*fp_y(i,j) |
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& - alfn*aln1*fn_y(i,j+1) |
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& + two*alfp*alfn*sm_o(i,j) + (alp1-alfp)*locTp |
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& + (aln1-alfn)*locTn |
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& ) |
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sm_xy(i,j) = alf1*sm_xy(i,j) + alfp*fp_xy(i,j) |
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& + alfn*fn_xy(i,j+1) |
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& + three*( alpmn*sm_x(i,j) - alp1*fp_x(i,j) |
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& + aln1*fn_x(i,j+1) |
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& ) |
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sm_yz(i,j) = alf1*sm_yz(i,j) + alfp*fp_yz(i,j) |
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& + alfn*fn_yz(i,j+1) |
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& + three*( alpmn*sm_z(i,j) - alp1*fp_z(i,j) |
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& + aln1*fn_z(i,j+1) |
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& ) |
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sm_y (i,j) = alf1*sm_y(i,j) + alfp*fp_y(i,j) + alfn*fn_y(i,j+1) |
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& + three*( locTp - locTn ) |
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sm_o (i,j) = sm_o (i,j) + fp_o (i,j) + fn_o (i,j+1) |
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sm_x (i,j) = sm_x (i,j) + fp_x (i,j) + fn_x (i,j+1) |
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sm_xx(i,j) = sm_xx(i,j) + fp_xx(i,j) + fn_xx(i,j+1) |
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sm_z (i,j) = sm_z (i,j) + fp_z (i,j) + fn_z (i,j+1) |
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sm_zz(i,j) = sm_zz(i,j) + fp_zz(i,j) + fn_zz(i,j+1) |
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sm_xz(i,j) = sm_xz(i,j) + fp_xz(i,j) + fn_xz(i,j+1) |
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ENDDO |
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ENDDO |
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|
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#endif /* GAD_ALLOW_SOM_ADVECT */ |
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|
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RETURN |
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END |
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