C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_som_adv_y.F,v 1.7 2013/03/02 00:29:20 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 overlapOnly, interiorOnly,
I N_edge, S_edge, E_edge, W_edge,
I deltaTloc, vTrans, maskIn,
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"
#include "EEPARAMS.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 overlapOnly :: only update the edges of myTile, but not the interior
C interiorOnly :: only update the interior of myTile, but not the edges
C [N,S,E,W]_edge :: true if N,S,E,W edge of myTile is an Edge of the cube
C vTrans :: zonal volume transport
C maskIn :: 2-D array Interior mask
C myThid :: my Thread Id. number
INTEGER bi,bj,k
INTEGER limiter
LOGICAL overlapOnly, interiorOnly
LOGICAL N_edge, S_edge, E_edge, W_edge
_RL deltaTloc
_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RS maskIn(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)
C !LOCAL VARIABLES: ====================================================
C i,j :: loop indices
C vLoc :: volume transported (per time step)
C [iMin,iMax]Upd :: loop range to update tracer field
C [jMin,jMax]Upd :: loop range to update tracer field
C nbStrips :: number of strips (if region to update is splitted)
_RL three
PARAMETER( three = 3. _d 0 )
INTEGER i,j
INTEGER ns, nbStrips
INTEGER iMinUpd(2), iMaxUpd(2), jMinUpd(2), jMaxUpd(2)
_RL recip_dT
_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
recip_dT = 0.
IF ( deltaTloc.GT.zeroRL ) recip_dT = 1.0 _d 0 / deltaTloc
C- Set loop ranges for updating tracer field (splitted in 2 strips)
nbStrips = 1
iMinUpd(1) = 1-OLx
iMaxUpd(1) = sNx+OLx
jMinUpd(1) = 1-OLy+1
jMaxUpd(1) = sNy+OLy-1
IF ( overlapOnly ) THEN
C update in overlap-Only
IF ( S_edge ) jMinUpd(1) = 1
IF ( N_edge ) jMaxUpd(1) = sNy
IF ( W_edge ) THEN
iMinUpd(1) = 1-OLx
iMaxUpd(1) = 0
ENDIF
IF ( E_edge ) THEN
IF ( W_edge ) nbStrips = 2
iMinUpd(nbStrips) = sNx+1
iMaxUpd(nbStrips) = sNx+OLx
ENDIF
ELSE
C do not only update the overlap
IF ( interiorOnly .AND. W_edge ) iMinUpd(1) = 1
IF ( interiorOnly .AND. E_edge ) iMaxUpd(1) = sNx
ENDIF
C-- start 1rst loop on strip number "ns"
DO ns=1,nbStrips
IF ( limiter.EQ.1 ) THEN
DO j=jMinUpd(1)-1,jMaxUpd(1)+1
DO i=iMinUpd(ns),iMaxUpd(ns)
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 j=jMinUpd(1),jMaxUpd(1)+1
DO i=iMinUpd(ns),iMaxUpd(ns)
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( zeroRL, 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( zeroRL, -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) )*recip_dT
ENDDO
ENDDO
C-- end 1rst loop on strip number "ns"
c ENDDO
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----|
C-- start 2nd loop on strip number "ns"
c DO ns=1,nbStrips
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=jMinUpd(1),jMaxUpd(1)
DO i=iMinUpd(ns),iMaxUpd(ns)
#ifdef ALLOW_OBCS
IF ( maskIn(i,j).NE.zeroRS ) THEN
#endif /* ALLOW_OBCS */
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)
#ifdef ALLOW_OBCS
ENDIF
#endif /* ALLOW_OBCS */
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=jMinUpd(1),jMaxUpd(1)
DO i=iMinUpd(ns),iMaxUpd(ns)
#ifdef ALLOW_OBCS
IF ( maskIn(i,j).NE.zeroRS ) THEN
#endif /* ALLOW_OBCS */
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)
& + twoRL*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)
#ifdef ALLOW_OBCS
ENDIF
#endif /* ALLOW_OBCS */
ENDDO
ENDDO
C-- end 2nd loop on strip number "ns"
ENDDO
RETURN
END