C $Header: /home/ubuntu/mnt/e9_copy/MITgcm/pkg/generic_advdiff/gad_som_adv_y.F,v 1.1 2007/01/16 04:38:34 jmc Exp $ C $Name: $ #include "GAD_OPTIONS.h" CBOP C !ROUTINE: GAD_SOM_ADV_Y C !INTERFACE: ========================================================== SUBROUTINE GAD_SOM_ADV_Y( I bi,bj,k, limiter, I deltaTloc, vTrans, U sm_v, sm_o, sm_x, sm_y, sm_z, U sm_xx, sm_yy, sm_zz, sm_xy, sm_xz, sm_yz, O vT, I myThid ) C !DESCRIPTION: C Calculates the area integrated meridional flux due to advection C of a tracer using C-- C Second-Order Moments Advection of tracer in Y-direction C ref: M.J.Prather, 1986, JGR, 91, D6, pp 6671-6681. C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| C The 3-D grid has dimension (Nx,Ny,Nz) with corresponding C velocity field (U,V,W). Parallel subroutine calculate C advection in the X- and Z- directions. C The moment [Si] are as defined in the text, Sm refers to C the total mass in each grid box C the moments [Fi] are similarly defined and used as temporary C storage for portions of the grid boxes in transit. C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| C !USES: =============================================================== IMPLICIT NONE #include "SIZE.h" c #include "GRID.h" #include "GAD.h" C !INPUT PARAMETERS: =================================================== C bi,bj :: tile indices C k :: vertical level C limiter :: 0: no limiter ; 1: Prather, 1986 limiter C vTrans :: zonal volume transport C myThid :: my Thread Id. number INTEGER bi,bj,k INTEGER limiter _RL deltaTloc _RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) c _RL tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy) INTEGER myThid C !OUTPUT PARAMETERS: ================================================== C sm_v :: volume of grid cell C sm_o :: tracer content of grid cell (zero order moment) C sm_x,y,z :: 1rst order moment of tracer distribution, in x,y,z direction C sm_xx,yy,zz :: 2nd order moment of tracer distribution, in x,y,z direction C sm_xy,xz,yz :: 2nd order moment of tracer distr., in cross direction xy,xz,yz C vT :: meridional advective flux _RL sm_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL sm_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL sm_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL sm_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL sm_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL sm_xx (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL sm_yy (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL sm_zz (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL sm_xy (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL sm_xz (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL sm_yz (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL vT (1-OLx:sNx+OLx,1-OLy:sNy+OLy) #ifdef GAD_ALLOW_SOM_ADVECT C !LOCAL VARIABLES: ==================================================== C i,j :: loop indices C vLoc :: volume transported (per time step) _RL two, three PARAMETER( two = 2. _d 0 ) PARAMETER( three = 3. _d 0 ) INTEGER i,j _RL slpmax, s1max, s1new, s2new _RL vLoc, alf1, alf1q, alpmn _RL alfp, alpq, alp1, locTp _RL alfn, alnq, aln1, locTn _RL alp (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL aln (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fp_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fn_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fp_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fn_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fp_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fn_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fp_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fn_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fp_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fn_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fp_xx(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fn_xx(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fp_yy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fn_yy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fp_zz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fn_zz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fp_xy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fn_xy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fp_xz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fn_xz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fp_yz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) _RL fn_yz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) CEOP IF ( limiter.EQ.1 ) THEN DO j=1-OLy,sNy+OLy DO i=1-OLx,sNx+OLx C If flux-limiting transport is to be applied, place limits on C appropriate moments before transport. slpmax = 0. IF ( sm_o(i,j).GT.0. ) slpmax = sm_o(i,j) s1max = slpmax*1.5 _d 0 s1new = MIN( s1max, MAX(-s1max,sm_y(i,j)) ) s2new = MIN( (slpmax+slpmax-ABS(s1new)/three), & MAX(ABS(s1new)-slpmax,sm_yy(i,j)) ) sm_xy(i,j) = MIN( slpmax, MAX(-slpmax,sm_xy(i,j)) ) sm_yz(i,j) = MIN( slpmax, MAX(-slpmax,sm_yz(i,j)) ) sm_y (i,j) = s1new ; sm_yy(i,j) = s2new ; ENDDO ENDDO ENDIF C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| C--- part.1 : calculate flux for all moments DO i=1-OLx,sNx+OLx vT(i,1-OLy)=0. ENDDO DO j=1-OLy+1,sNy+OLy DO i=1-OLx,sNx+OLx vLoc = vTrans(i,j)*deltaTloc C-- Flux from (j-1) to (j) when V>0 (i.e., take right side of box j-1) fp_v (i,j) = MAX( 0. _d 0, vLoc ) alp (i,j) = fp_v(i,j)/sm_v(i,j-1) alpq = alp(i,j)*alp(i,j) alp1 = 1. _d 0 - alp(i,j) C- Create temporary moments/masses for partial boxes in transit C use same indexing as velocity, "p" for positive V fp_o (i,j) = alp(i,j)*( sm_o(i,j-1) + alp1*sm_y(i,j-1) & + alp1*(alp1-alp(i,j))*sm_yy(i,j-1) & ) fp_y (i,j) = alpq *( sm_y(i,j-1) + three*alp1*sm_yy(i,j-1) ) fp_yy(i,j) = alp(i,j)*alpq*sm_yy(i,j-1) fp_x (i,j) = alp(i,j)*( sm_x(i,j-1) + alp1*sm_xy(i,j-1) ) fp_z (i,j) = alp(i,j)*( sm_z(i,j-1) + alp1*sm_yz(i,j-1) ) fp_xy(i,j) = alpq *sm_xy(i,j-1) fp_yz(i,j) = alpq *sm_yz(i,j-1) fp_xx(i,j) = alp(i,j)*sm_xx(i,j-1) fp_zz(i,j) = alp(i,j)*sm_zz(i,j-1) fp_xz(i,j) = alp(i,j)*sm_xz(i,j-1) C-- Flux from (j) to (j-1) when V<0 (i.e., take left side of box j) fn_v (i,j) = MAX( 0. _d 0, -vLoc ) aln (i,j) = fn_v(i,j)/sm_v(i, j ) alnq = aln(i,j)*aln(i,j) aln1 = 1. _d 0 - aln(i,j) C- Create temporary moments/masses for partial boxes in transit C use same indexing as velocity, "n" for negative V fn_o (i,j) = aln(i,j)*( sm_o(i, j ) - aln1*sm_y(i, j ) & + aln1*(aln1-aln(i,j))*sm_yy(i, j ) & ) fn_y (i,j) = alnq *( sm_y(i, j ) - three*aln1*sm_yy(i, j ) ) fn_yy(i,j) = aln(i,j)*alnq*sm_yy(i, j ) fn_x (i,j) = aln(i,j)*( sm_x(i, j ) - aln1*sm_xy(i, j ) ) fn_z (i,j) = aln(i,j)*( sm_z(i, j ) - aln1*sm_yz(i, j ) ) fn_xy(i,j) = alnq *sm_xy(i, j ) fn_yz(i,j) = alnq *sm_yz(i, j ) fn_xx(i,j) = aln(i,j)*sm_xx(i, j ) fn_zz(i,j) = aln(i,j)*sm_zz(i, j ) fn_xz(i,j) = aln(i,j)*sm_xz(i, j ) C-- Save zero-order flux: vT(i,j) = fp_o(i,j) - fn_o(i,j) ENDDO ENDDO C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| C--- part.2 : re-adjust moments remaining in the box C take off from grid box (j): negative V(j) and positive V(j+1) DO j=1-OLy+1,sNy+OLy-1 DO i=1-OLx,sNx+OLx alf1 = 1. _d 0 - aln(i,j) - alp(i,j+1) alf1q = alf1*alf1 alpmn = alp(i,j+1) - aln(i,j) sm_v (i,j) = sm_v (i,j) - fn_v (i,j) - fp_v (i,j+1) sm_o (i,j) = sm_o (i,j) - fn_o (i,j) - fp_o (i,j+1) sm_y (i,j) = alf1q*( sm_y(i,j) - three*alpmn*sm_yy(i,j) ) sm_yy(i,j) = alf1*alf1q*sm_yy(i,j) sm_xy(i,j) = alf1q*sm_xy(i,j) sm_yz(i,j) = alf1q*sm_yz(i,j) sm_x (i,j) = sm_x (i,j) - fn_x (i,j) - fp_x (i,j+1) sm_xx(i,j) = sm_xx(i,j) - fn_xx(i,j) - fp_xx(i,j+1) sm_z (i,j) = sm_z (i,j) - fn_z (i,j) - fp_z (i,j+1) sm_zz(i,j) = sm_zz(i,j) - fn_zz(i,j) - fp_zz(i,j+1) sm_xz(i,j) = sm_xz(i,j) - fn_xz(i,j) - fp_xz(i,j+1) ENDDO ENDDO C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| C--- part.3 : Put the temporary moments into appropriate neighboring boxes C add into grid box (j): positive V(j) and negative V(j+1) DO j=1-OLy+1,sNy+OLy-1 DO i=1-OLx,sNx+OLx sm_v (i,j) = sm_v (i,j) + fp_v (i,j) + fn_v (i,j+1) alfp = fp_v(i, j )/sm_v(i,j) alfn = fn_v(i,j+1)/sm_v(i,j) alf1 = 1. _d 0 - alfp - alfn alp1 = 1. _d 0 - alfp aln1 = 1. _d 0 - alfn alpmn = alfp - alfn locTp = alfp*sm_o(i,j) - alp1*fp_o(i,j) locTn = alfn*sm_o(i,j) - aln1*fn_o(i,j+1) sm_yy(i,j) = alf1*alf1*sm_yy(i,j) + alfp*alfp*fp_yy(i,j) & + alfn*alfn*fn_yy(i,j+1) & - 5. _d 0*(-alpmn*alf1*sm_y(i,j) + alfp*alp1*fp_y(i,j) & - alfn*aln1*fn_y(i,j+1) & + two*alfp*alfn*sm_o(i,j) + (alp1-alfp)*locTp & + (aln1-alfn)*locTn & ) sm_xy(i,j) = alf1*sm_xy(i,j) + alfp*fp_xy(i,j) & + alfn*fn_xy(i,j+1) & + three*( alpmn*sm_x(i,j) - alp1*fp_x(i,j) & + aln1*fn_x(i,j+1) & ) sm_yz(i,j) = alf1*sm_yz(i,j) + alfp*fp_yz(i,j) & + alfn*fn_yz(i,j+1) & + three*( alpmn*sm_z(i,j) - alp1*fp_z(i,j) & + aln1*fn_z(i,j+1) & ) sm_y (i,j) = alf1*sm_y(i,j) + alfp*fp_y(i,j) + alfn*fn_y(i,j+1) & + three*( locTp - locTn ) sm_o (i,j) = sm_o (i,j) + fp_o (i,j) + fn_o (i,j+1) sm_x (i,j) = sm_x (i,j) + fp_x (i,j) + fn_x (i,j+1) sm_xx(i,j) = sm_xx(i,j) + fp_xx(i,j) + fn_xx(i,j+1) sm_z (i,j) = sm_z (i,j) + fp_z (i,j) + fn_z (i,j+1) sm_zz(i,j) = sm_zz(i,j) + fp_zz(i,j) + fn_zz(i,j+1) sm_xz(i,j) = sm_xz(i,j) + fp_xz(i,j) + fn_xz(i,j+1) ENDDO ENDDO #endif /* GAD_ALLOW_SOM_ADVECT */ RETURN END