pkg/generic_advdiff/gad_os7mp_adv_y.F

C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_os7mp_adv_y.F,v 1.3 2007/04/04 01:39:06 jmc Exp $
C $Name:  $

#include "GAD_OPTIONS.h"

      SUBROUTINE GAD_OS7MP_ADV_Y(
     I           bi,bj,k, calcCFL, deltaTloc,
     I           vTrans, vFld,
     I           maskLocS, Q,
     O           vT,
     I           myThid )
C     /==========================================================\
C     | SUBROUTINE GAD_OS7MP_ADV_Y                               |
C     | o Compute Meridional advective Flux of tracer Q using    |
C     |   7th Order DST Sceheme with monotone preserving limiter |
C     |==========================================================|
      IMPLICIT NONE

C     == GLobal variables ==
#include "SIZE.h"
#include "GRID.h"
#include "GAD.h"

C     == Routine arguments ==
      INTEGER bi,bj,k
      LOGICAL calcCFL
      _RL deltaTloc
      _RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL vFld  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RS maskLocS(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL Q     (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL vT    (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      INTEGER myThid

C     == Local variables ==
      INTEGER i,j
      _RL cfl,Psi
      _RL vLoc,Fac,Del,DelIp,DelI,Phi,Eps,rp1h,rp1h_cfl,Msk
      _RL Qippp,Qipp,Qip,Qi,Qim,Qimm,Qimmm
      _RL MskIpp,MskIp,MskI,MskIm,MskImm,MskImmm
      _RL d2,d2p1,d2m1,A,B,C,D
      _RL dp1h,dm1h,qMD,qUL,qLC,PhiMD,PhiLC,PhiMin,PhiMax

      Eps = 1. _d -20

      DO i=1-Olx,sNx+Olx
       vT(i,1-Oly)=0. _d 0
       vT(i,2-Oly)=0. _d 0
       vT(i,3-Oly)=0. _d 0
       vT(i,4-Oly)=0. _d 0
       vT(i,sNy+Oly-2)=0. _d 0
       vT(i,sNy+Oly-1)=0. _d 0
       vT(i,sNy+Oly)=0. _d 0
      ENDDO
      DO j=1-Oly+4,sNy+Oly-3
       DO i=1-Olx,sNx+Olx

        vLoc = vFld(i,j)
        cfl = vLoc
        IF ( calcCFL ) cfl = abs(vLoc*deltaTloc*recip_dyC(i,j,bi,bj))

        IF (vTrans(i,j).gt.0.) THEN
         Qippp = Q(i,j+2)
         Qipp  = Q(i,j+1)
         Qip   = Q(i,j)
         Qi    = Q(i,j-1)
         Qim   = Q(i,j-2)
         Qimm  = Q(i,j-3)
         Qimmm = Q(i,j-4)

         MskIpp  = maskLocS(i,j+2)
         MskIp   = maskLocS(i,j+1)
         MskI    = maskLocS(i,j)
         MskIm   = maskLocS(i,j-1)
         MskImm  = maskLocS(i,j-2)
         MskImmm = maskLocS(i,j-3)
        ELSEIF (vTrans(i,j).lt.0.) THEN
         Qippp = Q(i,j-3)
         Qipp  = Q(i,j-2)
         Qip   = Q(i,j-1)
         Qi    = Q(i,j)
         Qim   = Q(i,j+1)
         Qimm  = Q(i,j+2)
         Qimmm = Q(i,j+3)

         MskIpp  = maskLocS(i,j-2)
         MskIp   = maskLocS(i,j-1)
         MskI    = maskLocS(i,j)
         MskIm   = maskLocS(i,j+1)
         MskImm  = maskLocS(i,j+2)
         MskImmm = maskLocS(i,j+3)
        ENDIF

        IF (vTrans(i,j).ne.0.) THEN
C        2nd order correction [i i-1]
         Fac = 1.
         Del = Qip-Qi
         Msk = MskI
         Phi = Msk * Fac * Del
C        3rd order correction [i i-1 i-2]
         Fac = Fac * ( cfl + 1. )/3.
         Del = Del - ( Qi-Qim )
         Msk = Msk * MskIm
         Phi = Phi - Msk * Fac * Del
C        4th order correction [i+1 i i-1 i-2]
         Fac = Fac * ( cfl - 2. )/4.
         Del = ( Qipp-2.*Qip+Qi ) - Del
         Msk = Msk * MskIp
         Phi = Phi + Msk * Fac * Del
C        5th order correction [i+1 i i-1 i-2 i-3]
         Fac = Fac * ( cfl - 3. )/5.
         Del = Del - ( Qip-3.*Qi+3.*Qim-Qimm )
         Msk = Msk * MskImm
         Phi = Phi + Msk * Fac * Del
C        6th order correction [i+2 i+1 i i-1 i-2 i-3]
         Fac = Fac * ( cfl + 2. )/6.
         Del = ( Qippp-4.*Qipp+6.*Qip-4.*Qi+Qim ) - Del
         Msk = Msk * MskIpp
         Phi = Phi + Msk * Fac * Del
C        7th order correction [i+2 i+1 i i-1 i-2 i-3 i-4]
         Fac = Fac * ( cfl + 2. )/7.
         Del = Del - ( Qipp-5.*Qip+10.*Qi-10.*Qim+5.*Qimm-Qimmm ) 
         Msk = Msk * MskImmm
         Phi = Phi - Msk * Fac * Del

         DelIp = ( Qip - Qi ) * MskI
         Phi = sign(1. _d 0,Phi)*sign(1. _d 0,DelIp)
     &        *abs(Phi+Eps)/abs(DelIp+Eps)

         DelI = ( Qi - Qim ) * MskIm
         rp1h =sign(1. _d 0,DelI)*sign(1. _d 0,DelIp)
     &        *abs(DelI+Eps)/abs(DelIp+Eps)
         rp1h_cfl = rp1h/(cfl+Eps)

C        TVD limiter
!        Phi = max(0. _d 0, min( 2./(1-cfl), Phi, 2.*rp1h_cfl ) )

C        MP limiter
         d2   = ( ( Qip + Qim ) - 2.*Qi  ) * MskI * MskIm
         d2p1 = ( ( Qipp + Qi ) - 2.*Qip ) * MskIp * MskI
         d2m1 = ( ( Qi + Qimm ) - 2.*Qim ) * MskIm * MskImm
         A = 4.*d2 - d2p1
         B = 4.*d2p1 - d2
         C = d2
         D = d2p1;
         dp1h = max(min(A,B,C,D),0. _d 0)+min(max(A,B,C,D),0. _d 0)
         A = 4.*d2m1 - d2
         B = 4.*d2 - d2m1
         C = d2m1
         D = d2;
         dm1h = max(min(A,B,C,D),0. _d 0)+min(max(A,B,C,D),0. _d 0)
         qMD = 0.5*( ( Qi + Qip ) - dp1h )
         qUL = Qi + (1.-cfl)/(cfl+Eps)*( Qi-Qim )
         qLC = Qi + 0.5*( 1.+dm1h/(Qi-Qim+Eps) )*(qUL-Qi)
         PhiMD = 2./(1.-cfl)*(qMD-Qi+Eps)/(Qip-Qi+Eps)
         PhiLC = 2.*rp1h_cfl*(qLC-Qi+Eps)/(qUL-Qi+Eps)
         PhiMin = max(min(0. _d 0,PhiMD),
     &        min(0. _d 0,2.*rp1h_cfl,PhiLC))
         PhiMax = min(max(2. _d 0/(1.-cfl),PhiMD),
     &        max(0. _d 0,2.*rp1h_cfl,PhiLC))
         Phi = max(PhiMin,min(Phi,PhiMax))

         Psi = Phi * 0.5 * (1. - cfl)
         vT(i,j) = vTrans(i,j)*( Qi + Psi*DelIp )
        ELSE
         vT(i,j) = 0.
        ENDIF

       ENDDO
      ENDDO

      RETURN
      END
1	adcroft	1.4	C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_os7mp_adv_y.F,v 1.3 2007/04/04 01:39:06 jmc Exp $
2	mlosch	1.2	C $Name: $
3	adcroft	1.1
4			#include "GAD_OPTIONS.h"
5
6			SUBROUTINE GAD_OS7MP_ADV_Y(
7	jmc	1.3	I bi,bj,k, calcCFL, deltaTloc,
8	adcroft	1.1	I vTrans, vFld,
9			I maskLocS, Q,
10			O vT,
11			I myThid )
12			C /==========================================================\
13			C \| SUBROUTINE GAD_OS7MP_ADV_Y \|
14			C \| o Compute Meridional advective Flux of tracer Q using \|
15			C \| 7th Order DST Sceheme with monotone preserving limiter \|
16			C \|==========================================================\|
17			IMPLICIT NONE
18
19			C == GLobal variables ==
20			#include "SIZE.h"
21			#include "GRID.h"
22			#include "GAD.h"
23
24			C == Routine arguments ==
25			INTEGER bi,bj,k
26	jmc	1.3	LOGICAL calcCFL
27	adcroft	1.1	_RL deltaTloc
28			_RL vTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
29			_RL vFld (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
30			_RS maskLocS(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
31			_RL Q (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
32			_RL vT (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
33			INTEGER myThid
34
35			C == Local variables ==
36			INTEGER i,j
37			_RL cfl,Psi
38	adcroft	1.4	_RL vLoc,Fac,Del,DelIp,DelI,Phi,Eps,rp1h,rp1h_cfl,Msk
39	adcroft	1.1	_RL Qippp,Qipp,Qip,Qi,Qim,Qimm,Qimmm
40			_RL MskIpp,MskIp,MskI,MskIm,MskImm,MskImmm
41			_RL d2,d2p1,d2m1,A,B,C,D
42			_RL dp1h,dm1h,qMD,qUL,qLC,PhiMD,PhiLC,PhiMin,PhiMax
43
44			Eps = 1. _d -20
45
46			DO i=1-Olx,sNx+Olx
47			vT(i,1-Oly)=0. _d 0
48			vT(i,2-Oly)=0. _d 0
49			vT(i,3-Oly)=0. _d 0
50			vT(i,4-Oly)=0. _d 0
51			vT(i,sNy+Oly-2)=0. _d 0
52			vT(i,sNy+Oly-1)=0. _d 0
53			vT(i,sNy+Oly)=0. _d 0
54			ENDDO
55			DO j=1-Oly+4,sNy+Oly-3
56			DO i=1-Olx,sNx+Olx
57
58			vLoc = vFld(i,j)
59	jmc	1.3	cfl = vLoc
60			IF ( calcCFL ) cfl = abs(vLocdeltaTlocrecip_dyC(i,j,bi,bj))
61	adcroft	1.1
62	adcroft	1.4	IF (vTrans(i,j).gt.0.) THEN
63	adcroft	1.1	Qippp = Q(i,j+2)
64			Qipp = Q(i,j+1)
65			Qip = Q(i,j)
66			Qi = Q(i,j-1)
67			Qim = Q(i,j-2)
68			Qimm = Q(i,j-3)
69			Qimmm = Q(i,j-4)
70
71			MskIpp = maskLocS(i,j+2)
72			MskIp = maskLocS(i,j+1)
73			MskI = maskLocS(i,j)
74			MskIm = maskLocS(i,j-1)
75			MskImm = maskLocS(i,j-2)
76			MskImmm = maskLocS(i,j-3)
77	adcroft	1.4	ELSEIF (vTrans(i,j).lt.0.) THEN
78	adcroft	1.1	Qippp = Q(i,j-3)
79			Qipp = Q(i,j-2)
80			Qip = Q(i,j-1)
81			Qi = Q(i,j)
82			Qim = Q(i,j+1)
83			Qimm = Q(i,j+2)
84			Qimmm = Q(i,j+3)
85
86			MskIpp = maskLocS(i,j-2)
87			MskIp = maskLocS(i,j-1)
88			MskI = maskLocS(i,j)
89			MskIm = maskLocS(i,j+1)
90			MskImm = maskLocS(i,j+2)
91			MskImmm = maskLocS(i,j+3)
92			ENDIF
93
94	adcroft	1.4	IF (vTrans(i,j).ne.0.) THEN
95	adcroft	1.1	C 2nd order correction [i i-1]
96			Fac = 1.
97			Del = Qip-Qi
98			Msk = MskI
99			Phi = Msk * Fac * Del
100			C 3rd order correction [i i-1 i-2]
101			Fac = Fac * ( cfl + 1. )/3.
102			Del = Del - ( Qi-Qim )
103			Msk = Msk * MskIm
104			Phi = Phi - Msk * Fac * Del
105			C 4th order correction [i+1 i i-1 i-2]
106			Fac = Fac * ( cfl - 2. )/4.
107			Del = ( Qipp-2.*Qip+Qi ) - Del
108			Msk = Msk * MskIp
109			Phi = Phi + Msk * Fac * Del
110			C 5th order correction [i+1 i i-1 i-2 i-3]
111			Fac = Fac * ( cfl - 3. )/5.
112			Del = Del - ( Qip-3.Qi+3.Qim-Qimm )
113			Msk = Msk * MskImm
114			Phi = Phi + Msk * Fac * Del
115			C 6th order correction [i+2 i+1 i i-1 i-2 i-3]
116			Fac = Fac * ( cfl + 2. )/6.
117			Del = ( Qippp-4.Qipp+6.Qip-4.*Qi+Qim ) - Del
118			Msk = Msk * MskIpp
119			Phi = Phi + Msk * Fac * Del
120			C 7th order correction [i+2 i+1 i i-1 i-2 i-3 i-4]
121			Fac = Fac * ( cfl + 2. )/7.
122			Del = Del - ( Qipp-5.Qip+10.Qi-10.Qim+5.Qimm-Qimmm )
123			Msk = Msk * MskImmm
124			Phi = Phi - Msk * Fac * Del
125
126			DelIp = ( Qip - Qi ) * MskI
127	mlosch	1.2	Phi = sign(1. _d 0,Phi)*sign(1. _d 0,DelIp)
128			& *abs(Phi+Eps)/abs(DelIp+Eps)
129	adcroft	1.1
130			DelI = ( Qi - Qim ) * MskIm
131	mlosch	1.2	rp1h =sign(1. _d 0,DelI)*sign(1. _d 0,DelIp)
132			& *abs(DelI+Eps)/abs(DelIp+Eps)
133	adcroft	1.4	rp1h_cfl = rp1h/(cfl+Eps)
134	adcroft	1.1
135			C TVD limiter
136	adcroft	1.4	! Phi = max(0. _d 0, min( 2./(1-cfl), Phi, 2.*rp1h_cfl ) )
137	adcroft	1.1
138			C MP limiter
139			d2 = ( ( Qip + Qim ) - 2.Qi ) MskI * MskIm
140			d2p1 = ( ( Qipp + Qi ) - 2.Qip ) MskIp * MskI
141			d2m1 = ( ( Qi + Qimm ) - 2.Qim ) MskIm * MskImm
142			A = 4.*d2 - d2p1
143			B = 4.*d2p1 - d2
144			C = d2
145			D = d2p1;
146	mlosch	1.2	dp1h = max(min(A,B,C,D),0. _d 0)+min(max(A,B,C,D),0. _d 0)
147	adcroft	1.1	A = 4.*d2m1 - d2
148			B = 4.*d2 - d2m1
149			C = d2m1
150			D = d2;
151	mlosch	1.2	dm1h = max(min(A,B,C,D),0. _d 0)+min(max(A,B,C,D),0. _d 0)
152	adcroft	1.1	qMD = 0.5*( ( Qi + Qip ) - dp1h )
153	adcroft	1.4	qUL = Qi + (1.-cfl)/(cfl+Eps)*( Qi-Qim )
154	adcroft	1.1	qLC = Qi + 0.5( 1.+dm1h/(Qi-Qim+Eps) )(qUL-Qi)
155			PhiMD = 2./(1.-cfl)*(qMD-Qi+Eps)/(Qip-Qi+Eps)
156	adcroft	1.4	PhiLC = 2.rp1h_cfl(qLC-Qi+Eps)/(qUL-Qi+Eps)
157	mlosch	1.2	PhiMin = max(min(0. _d 0,PhiMD),
158	adcroft	1.4	& min(0. _d 0,2.*rp1h_cfl,PhiLC))
159	mlosch	1.2	PhiMax = min(max(2. _d 0/(1.-cfl),PhiMD),
160	adcroft	1.4	& max(0. _d 0,2.*rp1h_cfl,PhiLC))
161	adcroft	1.1	Phi = max(PhiMin,min(Phi,PhiMax))
162
163			Psi = Phi * 0.5 * (1. - cfl)
164			vT(i,j) = vTrans(i,j)( Qi + PsiDelIp )
165			ELSE
166	adcroft	1.4	vT(i,j) = 0.
167	adcroft	1.1	ENDIF
168
169			ENDDO
170			ENDDO
171
172			RETURN
173			END