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gad_u3_adv_x.F
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gad_u3_adv_x.F
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#include "GAD_OPTIONS.h"
CBOP
C !ROUTINE: GAD_U3_ADV_X
C !INTERFACE: ==========================================================
SUBROUTINE GAD_U3_ADV_X(
I bi,bj,k,
I uTrans, maskLocW,
I tracer,
O uT,
I myThid )
C !DESCRIPTION:
C Calculates the area integrated zonal flux due to advection of a tracer
C using upwind biased third-order interpolation (or the $\kappa=1/3$ scheme):
C \begin{equation*}
C F^x_{adv} = U \overline{ \theta - \frac{1}{6} \delta_{ii} \theta }^i
C + \frac{1}{12} |U| \delta_{iii} \theta
C \end{equation*}
C Near boundaries, mask all the gradients ==> still 3rd O.
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 uTrans :: zonal volume transport
C maskLocW :: mask (either 0 or 1) at grid-cell western edge
C tracer :: tracer field
C myThid :: my thread Id number
INTEGER bi,bj,k
_RL uTrans (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RS maskLocW(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
_RL tracer (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
INTEGER myThid
C !OUTPUT PARAMETERS: ==================================================
C uT :: zonal advective flux
_RL uT (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
C !LOCAL VARIABLES: ====================================================
C i,j :: loop indices
C Rjm,Rj,Rjp :: differences at i-1,i,i+1
C Rjjm,Rjjp :: second differences at i-1,i
INTEGER i,j
_RL Rjm,Rj,Rjp,Rjjm,Rjjp
CEOP
DO j=1-Oly,sNy+Oly
uT(1-Olx,j)=0.
uT(2-Olx,j)=0.
uT(sNx+Olx,j)=0.
ENDDO
DO j=1-Oly,sNy+Oly
DO i=1-Olx+2,sNx+Olx-1
Rjp = (tracer(i+1,j)-tracer( i ,j))*maskLocW(i+1,j)
Rj = (tracer( i ,j)-tracer(i-1,j))*maskLocW( i ,j)
Rjm = (tracer(i-1,j)-tracer(i-2,j))*maskLocW(i-1,j)
Rjjp=Rjp-Rj
Rjjm=Rj-Rjm
uT(i,j) =
& uTrans(i,j)*(
& Tracer(i,j)+Tracer(i-1,j)-oneSixth*( Rjjp+Rjjm )
& )*0.5 _d 0
& +ABS( uTrans(i,j) )*0.5 _d 0*oneSixth*( Rjjp-Rjjm )
ENDDO
ENDDO
RETURN
END