pkg/generic_advdiff/gad_u3_adv_y.F

C $Header: /u/gcmpack/models/MITgcmUV/pkg/generic_advdiff/gad_u3_adv_y.F,v 1.3 2001/09/26 19:05:21 adcroft Exp $
C $Name:  $

#include "GAD_OPTIONS.h"

CBOP
C !ROUTINE: GAD_U3_ADV_Y

C !INTERFACE: ==========================================================
      SUBROUTINE GAD_U3_ADV_Y( 
     I           bi,bj,k,
     I           vTrans,
     I           tracer,
     O           vT,
     I           myThid )

C !DESCRIPTION:
C Calculates the area integrated meridional 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^y_{adv} = V \overline{ \theta  - \frac{1}{6} \delta_{jj} \theta }^j
C                 + \frac{1}{12} |V| \delta_{jjj} \theta
C \end{equation*}
C Near boundaries, mask all the gradients ==> still 3rd O.

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  vTrans               :: meridional volume transport
C  tracer               :: tracer field
C  myThid               :: thread number
      INTEGER bi,bj,k
      _RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      INTEGER myThid

C !OUTPUT PARAMETERS: ==================================================
C  vT                   :: meridional advective flux
      _RL vT    (1-OLx:sNx+OLx,1-OLy:sNy+OLy)

C !LOCAL VARIABLES: ====================================================
C  i,j                  :: loop indices
C  Rjm,Rj,Rjp           :: differences at j-1,j,j+1
C  Rjjm,Rjjp            :: second differences at j-1,j
      INTEGER i,j
      _RL Rjm,Rj,Rjp,Rjjm,Rjjp
CEOP

      DO i=1-Olx,sNx+Olx
       vT(i,1-Oly)=0.
       vT(i,2-Oly)=0.
       vT(i,sNy+Oly)=0.
      ENDDO
      DO j=1-Oly+2,sNy+Oly-1
       DO i=1-Olx,sNx+Olx
        Rjp=(tracer(i,j+1)-tracer(i,j))*maskS(i,j+1,k,bi,bj)
        Rj =(tracer(i,j)-tracer(i,j-1))*maskS(i,j,k,bi,bj)
        Rjm=(tracer(i,j-1)-tracer(i,j-2))*maskS(i,j-1,k,bi,bj)
        Rjjp=Rjp-Rj
        Rjjm=Rj-Rjm
        vT(i,j) = 
     &   vTrans(i,j)*(
     &     Tracer(i,j)+Tracer(i,j-1)-oneSixth*( Rjjp+Rjjm )
     &               )*0.5 _d 0
     &  +ABS( vTrans(i,j) )*0.5 _d 0*oneSixth*( Rjjp-Rjjm )
       ENDDO
      ENDDO

      RETURN
      END
1	C $Header: /u/gcmpack/models/MITgcmUV/pkg/generic_advdiff/gad_u3_adv_y.F,v 1.3 2001/09/26 19:05:21 adcroft Exp $
2	C $Name: $
3
4	#include "GAD_OPTIONS.h"
5
6	CBOP
7	C !ROUTINE: GAD_U3_ADV_Y
8
9	C !INTERFACE: ==========================================================
10	SUBROUTINE GAD_U3_ADV_Y(
11	I bi,bj,k,
12	I vTrans,
13	I tracer,
14	O vT,
15	I myThid )
16
17	C !DESCRIPTION:
18	C Calculates the area integrated meridional flux due to advection of a tracer
19	C using upwind biased third-order interpolation (or the $\kappa=1/3$ scheme):
20	C \begin{equation*}
21	C F^y_{adv} = V \overline{ \theta - \frac{1}{6} \delta_{jj} \theta }^j
22	C + \frac{1}{12} \|V\| \delta_{jjj} \theta
23	C \end{equation*}
24	C Near boundaries, mask all the gradients ==> still 3rd O.
25
26	C !USES: ===============================================================
27	IMPLICIT NONE
28	#include "SIZE.h"
29	#include "GRID.h"
30	#include "GAD.h"
31
32	C !INPUT PARAMETERS: ===================================================
33	C bi,bj :: tile indices
34	C k :: vertical level
35	C vTrans :: meridional volume transport
36	C tracer :: tracer field
37	C myThid :: thread number
38	INTEGER bi,bj,k
39	_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
40	_RL tracer(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
41	INTEGER myThid
42
43	C !OUTPUT PARAMETERS: ==================================================
44	C vT :: meridional advective flux
45	_RL vT (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
46
47	C !LOCAL VARIABLES: ====================================================
48	C i,j :: loop indices
49	C Rjm,Rj,Rjp :: differences at j-1,j,j+1
50	C Rjjm,Rjjp :: second differences at j-1,j
51	INTEGER i,j
52	_RL Rjm,Rj,Rjp,Rjjm,Rjjp
53	CEOP
54
55	DO i=1-Olx,sNx+Olx
56	vT(i,1-Oly)=0.
57	vT(i,2-Oly)=0.
58	vT(i,sNy+Oly)=0.
59	ENDDO
60	DO j=1-Oly+2,sNy+Oly-1
61	DO i=1-Olx,sNx+Olx
62	Rjp=(tracer(i,j+1)-tracer(i,j))*maskS(i,j+1,k,bi,bj)
63	Rj =(tracer(i,j)-tracer(i,j-1))*maskS(i,j,k,bi,bj)
64	Rjm=(tracer(i,j-1)-tracer(i,j-2))*maskS(i,j-1,k,bi,bj)
65	Rjjp=Rjp-Rj
66	Rjjm=Rj-Rjm
67	vT(i,j) =
68	& vTrans(i,j)*(
69	& Tracer(i,j)+Tracer(i,j-1)-oneSixth*( Rjjp+Rjjm )
70	& )*0.5 _d 0
71	& +ABS( vTrans(i,j) )0.5 _d 0oneSixth*( Rjjp-Rjjm )
72	ENDDO
73	ENDDO
74
75	RETURN
76	END