C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_c4_adv_r.F,v 1.6 2014/08/18 12:22:46 jmc Exp $
C $Name: $
#include "GAD_OPTIONS.h"
CBOP
C !ROUTINE: GAD_C4_ADV_R
C !INTERFACE: ==========================================================
SUBROUTINE GAD_C4_ADV_R(
I bi, bj, k,
I rTrans,
I tracer,
O wT,
I myThid )
C !DESCRIPTION:
C Calculates the area integrated vertical flux due to advection of a tracer
C using centered fourth-order interpolation:
C \begin{equation*}
C F^r_{adv} = W \overline{ \theta - \frac{1}{6} \delta_{kk} \theta }^k
C \end{equation*}
C Near boundaries, the scheme reduces to a second if the flow is away
C from the boundary and to third order if the flow is towards
C the boundary.
C !USES: ===============================================================
IMPLICIT NONE
#include "SIZE.h"
#include "GRID.h"
#include "GAD.h"
C !INPUT PARAMETERS: ===================================================
C bi,bj :: tile indices
C k :: vertical level
C rTrans :: vertical volume transport
C tracer :: tracer field
C myThid :: thread number
INTEGER bi,bj,k
_RL rTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy,Nr)
INTEGER myThid
C !OUTPUT PARAMETERS: ==================================================
C wT :: vertical advective flux
_RL wT (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
C !LOCAL VARIABLES: ====================================================
C i,j :: loop indices
C kp1 :: =min( k+1 , Nr )
C km1 :: =max( k-1 , 1 )
C km2 :: =max( k-2 , 1 )
C Rjm,Rj,Rjp :: differences at i-1,i,i+1
C Rjjm,Rjjp :: second differences at i-1,i
C maskP1 :: =1 for k=Nr
INTEGER i,j,kp1,km1,km2
_RL Rjm,Rj,Rjp,Rjjm,Rjjp
_RL maskPM, maskBound
CEOP
km2=MAX(1,k-2)
km1=MAX(1,k-1)
kp1=MIN(Nr,k+1)
maskPM = 1.
IF (k.LE.2 .OR. k.GE.Nr) maskPM = 0.
IF ( k.EQ.1 .OR. k.GT.Nr) THEN
DO j=1-OLy,sNy+OLy
DO i=1-OLx,sNx+OLx
wT(i,j) = 0.
ENDDO
ENDDO
ELSE
DO j=1-OLy,sNy+OLy
DO i=1-OLx,sNx+OLx
maskBound = maskPM*maskC(i,j,km2,bi,bj)*maskC(i,j,kp1,bi,bj)
Rjp = (tracer(i,j,kp1)-tracer(i,j, k ))*maskC(i,j,kp1,bi,bj)
Rj = (tracer(i,j, k )-tracer(i,j,km1))
Rjm = (tracer(i,j,km1)-tracer(i,j,km2))*maskC(i,j,km1,bi,bj)
&
Rjjp=(Rjp-Rj)
Rjjm=(Rj-Rjm)
wT(i,j) = maskC(i,j,km1,bi,bj)*(
& rTrans(i,j)*( (tracer(i,j,k)+tracer(i,j,km1))*0.5 _d 0
& -oneSixth*(Rjjm+Rjjp)*0.5 _d 0 )
& +ABS(rTrans(i,j))*
& oneSixth*(Rjjm-Rjjp)*0.5 _d 0
& *(1. _d 0 - maskBound)
& )
ENDDO
ENDDO
ENDIF
RETURN
END