| 1 |
C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_som_adv_y.F,v 1.4 2008/02/12 20:32:34 jmc Exp $ |
| 2 |
C $Name: $ |
| 3 |
|
| 4 |
#include "GAD_OPTIONS.h" |
| 5 |
|
| 6 |
CBOP |
| 7 |
C !ROUTINE: GAD_SOM_ADV_Y |
| 8 |
|
| 9 |
C !INTERFACE: ========================================================== |
| 10 |
SUBROUTINE GAD_SOM_ADV_Y( |
| 11 |
I bi,bj,k, limiter, |
| 12 |
I overlapOnly, interiorOnly, |
| 13 |
I N_edge, S_edge, E_edge, W_edge, |
| 14 |
I deltaTloc, vTrans, |
| 15 |
U sm_v, sm_o, sm_x, sm_y, sm_z, |
| 16 |
U sm_xx, sm_yy, sm_zz, sm_xy, sm_xz, sm_yz, |
| 17 |
O vT, |
| 18 |
I myThid ) |
| 19 |
|
| 20 |
C !DESCRIPTION: |
| 21 |
C Calculates the area integrated meridional flux due to advection |
| 22 |
C of a tracer using |
| 23 |
C-- |
| 24 |
C Second-Order Moments Advection of tracer in Y-direction |
| 25 |
C ref: M.J.Prather, 1986, JGR, 91, D6, pp 6671-6681. |
| 26 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 27 |
C The 3-D grid has dimension (Nx,Ny,Nz) with corresponding |
| 28 |
C velocity field (U,V,W). Parallel subroutine calculate |
| 29 |
C advection in the X- and Z- directions. |
| 30 |
C The moment [Si] are as defined in the text, Sm refers to |
| 31 |
C the total mass in each grid box |
| 32 |
C the moments [Fi] are similarly defined and used as temporary |
| 33 |
C storage for portions of the grid boxes in transit. |
| 34 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 35 |
|
| 36 |
C !USES: =============================================================== |
| 37 |
IMPLICIT NONE |
| 38 |
#include "SIZE.h" |
| 39 |
#include "GAD.h" |
| 40 |
|
| 41 |
C !INPUT PARAMETERS: =================================================== |
| 42 |
C bi,bj :: tile indices |
| 43 |
C k :: vertical level |
| 44 |
C limiter :: 0: no limiter ; 1: Prather, 1986 limiter |
| 45 |
C overlapOnly :: only update the edges of myTile, but not the interior |
| 46 |
C interiorOnly :: only update the interior of myTile, but not the edges |
| 47 |
C [N,S,E,W]_edge :: true if N,S,E,W edge of myTile is an Edge of the cube |
| 48 |
C vTrans :: zonal volume transport |
| 49 |
C myThid :: my Thread Id. number |
| 50 |
INTEGER bi,bj,k |
| 51 |
INTEGER limiter |
| 52 |
LOGICAL overlapOnly, interiorOnly |
| 53 |
LOGICAL N_edge, S_edge, E_edge, W_edge |
| 54 |
_RL deltaTloc |
| 55 |
_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 56 |
INTEGER myThid |
| 57 |
|
| 58 |
C !OUTPUT PARAMETERS: ================================================== |
| 59 |
C sm_v :: volume of grid cell |
| 60 |
C sm_o :: tracer content of grid cell (zero order moment) |
| 61 |
C sm_x,y,z :: 1rst order moment of tracer distribution, in x,y,z direction |
| 62 |
C sm_xx,yy,zz :: 2nd order moment of tracer distribution, in x,y,z direction |
| 63 |
C sm_xy,xz,yz :: 2nd order moment of tracer distr., in cross direction xy,xz,yz |
| 64 |
C vT :: meridional advective flux |
| 65 |
_RL sm_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 66 |
_RL sm_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 67 |
_RL sm_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 68 |
_RL sm_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 69 |
_RL sm_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 70 |
_RL sm_xx (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 71 |
_RL sm_yy (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 72 |
_RL sm_zz (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 73 |
_RL sm_xy (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 74 |
_RL sm_xz (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 75 |
_RL sm_yz (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 76 |
_RL vT (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 77 |
|
| 78 |
C !LOCAL VARIABLES: ==================================================== |
| 79 |
C i,j :: loop indices |
| 80 |
C vLoc :: volume transported (per time step) |
| 81 |
C [iMin,iMax]Upd :: loop range to update tracer field |
| 82 |
C [jMin,jMax]Upd :: loop range to update tracer field |
| 83 |
C nbStrips :: number of strips (if region to update is splitted) |
| 84 |
_RL two, three |
| 85 |
PARAMETER( two = 2. _d 0 ) |
| 86 |
PARAMETER( three = 3. _d 0 ) |
| 87 |
INTEGER i,j |
| 88 |
INTEGER ns, nbStrips |
| 89 |
INTEGER iMinUpd(2), iMaxUpd(2), jMinUpd(2), jMaxUpd(2) |
| 90 |
_RL recip_dT |
| 91 |
_RL slpmax, s1max, s1new, s2new |
| 92 |
_RL vLoc, alf1, alf1q, alpmn |
| 93 |
_RL alfp, alpq, alp1, locTp |
| 94 |
_RL alfn, alnq, aln1, locTn |
| 95 |
_RL alp (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 96 |
_RL aln (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 97 |
_RL fp_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 98 |
_RL fn_v (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 99 |
_RL fp_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 100 |
_RL fn_o (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 101 |
_RL fp_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 102 |
_RL fn_x (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 103 |
_RL fp_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 104 |
_RL fn_y (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 105 |
_RL fp_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 106 |
_RL fn_z (1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 107 |
_RL fp_xx(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 108 |
_RL fn_xx(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 109 |
_RL fp_yy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 110 |
_RL fn_yy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 111 |
_RL fp_zz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 112 |
_RL fn_zz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 113 |
_RL fp_xy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 114 |
_RL fn_xy(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 115 |
_RL fp_xz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 116 |
_RL fn_xz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 117 |
_RL fp_yz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 118 |
_RL fn_yz(1-OLx:sNx+OLx,1-OLy:sNy+OLy) |
| 119 |
CEOP |
| 120 |
|
| 121 |
recip_dT = 0. |
| 122 |
IF ( deltaTloc.GT.0. _d 0 ) recip_dT = 1.0 _d 0 / deltaTloc |
| 123 |
|
| 124 |
C- Set loop ranges for updating tracer field (splitted in 2 strips) |
| 125 |
nbStrips = 1 |
| 126 |
iMinUpd(1) = 1-Olx |
| 127 |
iMaxUpd(1) = sNx+Olx |
| 128 |
jMinUpd(1) = 1-Oly+1 |
| 129 |
jMaxUpd(1) = sNy+Oly-1 |
| 130 |
IF ( overlapOnly ) THEN |
| 131 |
C update in overlap-Only |
| 132 |
IF ( S_edge ) jMinUpd(1) = 1 |
| 133 |
IF ( N_edge ) jMaxUpd(1) = sNy |
| 134 |
IF ( W_edge ) THEN |
| 135 |
iMinUpd(1) = 1-Olx |
| 136 |
iMaxUpd(1) = 0 |
| 137 |
ENDIF |
| 138 |
IF ( E_edge ) THEN |
| 139 |
IF ( W_edge ) nbStrips = 2 |
| 140 |
iMinUpd(nbStrips) = sNx+1 |
| 141 |
iMaxUpd(nbStrips) = sNx+Olx |
| 142 |
ENDIF |
| 143 |
ELSE |
| 144 |
C do not only update the overlap |
| 145 |
IF ( interiorOnly .AND. W_edge ) iMinUpd(1) = 1 |
| 146 |
IF ( interiorOnly .AND. E_edge ) iMaxUpd(1) = sNx |
| 147 |
ENDIF |
| 148 |
|
| 149 |
C- Internal exchange for calculations in Y |
| 150 |
c IF ( overlapOnly ) THEN |
| 151 |
c CALL GAD_SOM_FILL_CS_CORNER( .FALSE., |
| 152 |
c U sm_v, sm_o, sm_x, sm_y, sm_z, |
| 153 |
c U sm_xx, sm_yy, sm_zz, sm_xy, sm_xz, sm_yz, |
| 154 |
c I bi, bj, myThid ) |
| 155 |
c ENDIF |
| 156 |
|
| 157 |
C-- start 1rst loop on strip number "ns" |
| 158 |
DO ns=1,nbStrips |
| 159 |
|
| 160 |
IF ( limiter.EQ.1 ) THEN |
| 161 |
DO j=jMinUpd(1)-1,jMaxUpd(1)+1 |
| 162 |
DO i=iMinUpd(ns),iMaxUpd(ns) |
| 163 |
C If flux-limiting transport is to be applied, place limits on |
| 164 |
C appropriate moments before transport. |
| 165 |
slpmax = 0. |
| 166 |
IF ( sm_o(i,j).GT.0. ) slpmax = sm_o(i,j) |
| 167 |
s1max = slpmax*1.5 _d 0 |
| 168 |
s1new = MIN( s1max, MAX(-s1max,sm_y(i,j)) ) |
| 169 |
s2new = MIN( (slpmax+slpmax-ABS(s1new)/three), |
| 170 |
& MAX(ABS(s1new)-slpmax,sm_yy(i,j)) ) |
| 171 |
sm_xy(i,j) = MIN( slpmax, MAX(-slpmax,sm_xy(i,j)) ) |
| 172 |
sm_yz(i,j) = MIN( slpmax, MAX(-slpmax,sm_yz(i,j)) ) |
| 173 |
sm_y (i,j) = s1new |
| 174 |
sm_yy(i,j) = s2new |
| 175 |
ENDDO |
| 176 |
ENDDO |
| 177 |
ENDIF |
| 178 |
|
| 179 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 180 |
C--- part.1 : calculate flux for all moments |
| 181 |
DO j=jMinUpd(1),jMaxUpd(1)+1 |
| 182 |
DO i=iMinUpd(ns),iMaxUpd(ns) |
| 183 |
vLoc = vTrans(i,j)*deltaTloc |
| 184 |
C-- Flux from (j-1) to (j) when V>0 (i.e., take right side of box j-1) |
| 185 |
fp_v (i,j) = MAX( 0. _d 0, vLoc ) |
| 186 |
alp (i,j) = fp_v(i,j)/sm_v(i,j-1) |
| 187 |
alpq = alp(i,j)*alp(i,j) |
| 188 |
alp1 = 1. _d 0 - alp(i,j) |
| 189 |
C- Create temporary moments/masses for partial boxes in transit |
| 190 |
C use same indexing as velocity, "p" for positive V |
| 191 |
fp_o (i,j) = alp(i,j)*( sm_o(i,j-1) + alp1*sm_y(i,j-1) |
| 192 |
& + alp1*(alp1-alp(i,j))*sm_yy(i,j-1) |
| 193 |
& ) |
| 194 |
fp_y (i,j) = alpq *( sm_y(i,j-1) + three*alp1*sm_yy(i,j-1) ) |
| 195 |
fp_yy(i,j) = alp(i,j)*alpq*sm_yy(i,j-1) |
| 196 |
fp_x (i,j) = alp(i,j)*( sm_x(i,j-1) + alp1*sm_xy(i,j-1) ) |
| 197 |
fp_z (i,j) = alp(i,j)*( sm_z(i,j-1) + alp1*sm_yz(i,j-1) ) |
| 198 |
|
| 199 |
fp_xy(i,j) = alpq *sm_xy(i,j-1) |
| 200 |
fp_yz(i,j) = alpq *sm_yz(i,j-1) |
| 201 |
fp_xx(i,j) = alp(i,j)*sm_xx(i,j-1) |
| 202 |
fp_zz(i,j) = alp(i,j)*sm_zz(i,j-1) |
| 203 |
fp_xz(i,j) = alp(i,j)*sm_xz(i,j-1) |
| 204 |
C-- Flux from (j) to (j-1) when V<0 (i.e., take left side of box j) |
| 205 |
fn_v (i,j) = MAX( 0. _d 0, -vLoc ) |
| 206 |
aln (i,j) = fn_v(i,j)/sm_v(i, j ) |
| 207 |
alnq = aln(i,j)*aln(i,j) |
| 208 |
aln1 = 1. _d 0 - aln(i,j) |
| 209 |
C- Create temporary moments/masses for partial boxes in transit |
| 210 |
C use same indexing as velocity, "n" for negative V |
| 211 |
fn_o (i,j) = aln(i,j)*( sm_o(i, j ) - aln1*sm_y(i, j ) |
| 212 |
& + aln1*(aln1-aln(i,j))*sm_yy(i, j ) |
| 213 |
& ) |
| 214 |
fn_y (i,j) = alnq *( sm_y(i, j ) - three*aln1*sm_yy(i, j ) ) |
| 215 |
fn_yy(i,j) = aln(i,j)*alnq*sm_yy(i, j ) |
| 216 |
fn_x (i,j) = aln(i,j)*( sm_x(i, j ) - aln1*sm_xy(i, j ) ) |
| 217 |
fn_z (i,j) = aln(i,j)*( sm_z(i, j ) - aln1*sm_yz(i, j ) ) |
| 218 |
fn_xy(i,j) = alnq *sm_xy(i, j ) |
| 219 |
fn_yz(i,j) = alnq *sm_yz(i, j ) |
| 220 |
fn_xx(i,j) = aln(i,j)*sm_xx(i, j ) |
| 221 |
fn_zz(i,j) = aln(i,j)*sm_zz(i, j ) |
| 222 |
fn_xz(i,j) = aln(i,j)*sm_xz(i, j ) |
| 223 |
C-- Save zero-order flux: |
| 224 |
vT(i,j) = ( fp_o(i,j) - fn_o(i,j) )*recip_dT |
| 225 |
ENDDO |
| 226 |
ENDDO |
| 227 |
|
| 228 |
C-- end 1rst loop on strip number "ns" |
| 229 |
c ENDDO |
| 230 |
|
| 231 |
C- Internal exchange for next calculations in X |
| 232 |
c IF ( overlapOnly ) THEN |
| 233 |
c CALL GAD_SOM_FILL_CS_CORNER( .TRUE., |
| 234 |
c U sm_v, sm_o, sm_x, sm_y, sm_z, |
| 235 |
c U sm_xx, sm_yy, sm_zz, sm_xy, sm_xz, sm_yz, |
| 236 |
c I bi, bj, myThid ) |
| 237 |
c ENDIF |
| 238 |
|
| 239 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 240 |
C-- start 2nd loop on strip number "ns" |
| 241 |
c DO ns=1,nbStrips |
| 242 |
|
| 243 |
C--- part.2 : re-adjust moments remaining in the box |
| 244 |
C take off from grid box (j): negative V(j) and positive V(j+1) |
| 245 |
DO j=jMinUpd(1),jMaxUpd(1) |
| 246 |
DO i=iMinUpd(ns),iMaxUpd(ns) |
| 247 |
alf1 = 1. _d 0 - aln(i,j) - alp(i,j+1) |
| 248 |
alf1q = alf1*alf1 |
| 249 |
alpmn = alp(i,j+1) - aln(i,j) |
| 250 |
sm_v (i,j) = sm_v (i,j) - fn_v (i,j) - fp_v (i,j+1) |
| 251 |
sm_o (i,j) = sm_o (i,j) - fn_o (i,j) - fp_o (i,j+1) |
| 252 |
sm_y (i,j) = alf1q*( sm_y(i,j) - three*alpmn*sm_yy(i,j) ) |
| 253 |
sm_yy(i,j) = alf1*alf1q*sm_yy(i,j) |
| 254 |
sm_xy(i,j) = alf1q*sm_xy(i,j) |
| 255 |
sm_yz(i,j) = alf1q*sm_yz(i,j) |
| 256 |
sm_x (i,j) = sm_x (i,j) - fn_x (i,j) - fp_x (i,j+1) |
| 257 |
sm_xx(i,j) = sm_xx(i,j) - fn_xx(i,j) - fp_xx(i,j+1) |
| 258 |
sm_z (i,j) = sm_z (i,j) - fn_z (i,j) - fp_z (i,j+1) |
| 259 |
sm_zz(i,j) = sm_zz(i,j) - fn_zz(i,j) - fp_zz(i,j+1) |
| 260 |
sm_xz(i,j) = sm_xz(i,j) - fn_xz(i,j) - fp_xz(i,j+1) |
| 261 |
ENDDO |
| 262 |
ENDDO |
| 263 |
|
| 264 |
C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
| 265 |
C--- part.3 : Put the temporary moments into appropriate neighboring boxes |
| 266 |
C add into grid box (j): positive V(j) and negative V(j+1) |
| 267 |
DO j=jMinUpd(1),jMaxUpd(1) |
| 268 |
DO i=iMinUpd(ns),iMaxUpd(ns) |
| 269 |
sm_v (i,j) = sm_v (i,j) + fp_v (i,j) + fn_v (i,j+1) |
| 270 |
alfp = fp_v(i, j )/sm_v(i,j) |
| 271 |
alfn = fn_v(i,j+1)/sm_v(i,j) |
| 272 |
alf1 = 1. _d 0 - alfp - alfn |
| 273 |
alp1 = 1. _d 0 - alfp |
| 274 |
aln1 = 1. _d 0 - alfn |
| 275 |
alpmn = alfp - alfn |
| 276 |
locTp = alfp*sm_o(i,j) - alp1*fp_o(i,j) |
| 277 |
locTn = alfn*sm_o(i,j) - aln1*fn_o(i,j+1) |
| 278 |
sm_yy(i,j) = alf1*alf1*sm_yy(i,j) + alfp*alfp*fp_yy(i,j) |
| 279 |
& + alfn*alfn*fn_yy(i,j+1) |
| 280 |
& - 5. _d 0*(-alpmn*alf1*sm_y(i,j) + alfp*alp1*fp_y(i,j) |
| 281 |
& - alfn*aln1*fn_y(i,j+1) |
| 282 |
& + two*alfp*alfn*sm_o(i,j) + (alp1-alfp)*locTp |
| 283 |
& + (aln1-alfn)*locTn |
| 284 |
& ) |
| 285 |
sm_xy(i,j) = alf1*sm_xy(i,j) + alfp*fp_xy(i,j) |
| 286 |
& + alfn*fn_xy(i,j+1) |
| 287 |
& + three*( alpmn*sm_x(i,j) - alp1*fp_x(i,j) |
| 288 |
& + aln1*fn_x(i,j+1) |
| 289 |
& ) |
| 290 |
sm_yz(i,j) = alf1*sm_yz(i,j) + alfp*fp_yz(i,j) |
| 291 |
& + alfn*fn_yz(i,j+1) |
| 292 |
& + three*( alpmn*sm_z(i,j) - alp1*fp_z(i,j) |
| 293 |
& + aln1*fn_z(i,j+1) |
| 294 |
& ) |
| 295 |
sm_y (i,j) = alf1*sm_y(i,j) + alfp*fp_y(i,j) + alfn*fn_y(i,j+1) |
| 296 |
& + three*( locTp - locTn ) |
| 297 |
sm_o (i,j) = sm_o (i,j) + fp_o (i,j) + fn_o (i,j+1) |
| 298 |
sm_x (i,j) = sm_x (i,j) + fp_x (i,j) + fn_x (i,j+1) |
| 299 |
sm_xx(i,j) = sm_xx(i,j) + fp_xx(i,j) + fn_xx(i,j+1) |
| 300 |
sm_z (i,j) = sm_z (i,j) + fp_z (i,j) + fn_z (i,j+1) |
| 301 |
sm_zz(i,j) = sm_zz(i,j) + fp_zz(i,j) + fn_zz(i,j+1) |
| 302 |
sm_xz(i,j) = sm_xz(i,j) + fp_xz(i,j) + fn_xz(i,j+1) |
| 303 |
ENDDO |
| 304 |
ENDDO |
| 305 |
|
| 306 |
C-- end 2nd loop on strip number "ns" |
| 307 |
ENDDO |
| 308 |
|
| 309 |
RETURN |
| 310 |
END |
Parent Directory
| 
Revision Log
| 
Revision Graph