pkg/generic_advdiff/gad_os7mp_adv_x.F

C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_os7mp_adv_x.F,v 1.1 2007/01/20 21:20:11 adcroft Exp $
C $Name:  $

#include "GAD_OPTIONS.h"

      SUBROUTINE GAD_OS7MP_ADV_X(
     I           bi,bj,k,deltaTloc,
     I           uTrans, uFld,
     I           maskLocW, Q,
     O           uT,
     I           myThid )
C     /==========================================================\
C     | SUBROUTINE GAD_OS7MP_ADV_X                               |
C     | o Compute Zonal 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
      _RL deltaTloc
      _RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL uFld  (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RS maskLocW(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL Q     (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      _RL uT    (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
      INTEGER myThid

C     == Local variables ==
      INTEGER i,j
      _RL cfl,Psi
      _RL uLoc,Fac,Del,DelIp,DelI,Phi,Eps,rp1h,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 j=1-Oly,sNy+Oly
       uT(1-Olx,j)=0. _d 0
       uT(2-Olx,j)=0. _d 0
       uT(3-Olx,j)=0. _d 0
       uT(4-Olx,j)=0. _d 0
       uT(sNx+Olx-2,j)=0. _d 0
       uT(sNx+Olx-1,j)=0. _d 0
       uT(sNx+Olx,j)=0. _d 0
       DO i=1-Olx+4,sNx+Olx-3

        uLoc = uFld(i,j)
        cfl = abs(uLoc*deltaTloc*recip_dxC(i,j,bi,bj))

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

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

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

        IF (uLoc.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)

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*( 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)
         uT(i,j) = uTrans(i,j)*( Qi + Psi*DelIp )
        ELSE
         uT(i,j) = 0.
        ENDIF

       ENDDO
      ENDDO

      RETURN
      END
1	mlosch	1.2	C $Header: /u/gcmpack/MITgcm/pkg/generic_advdiff/gad_os7mp_adv_x.F,v 1.1 2007/01/20 21:20:11 adcroft Exp $
2			C $Name: $
3	adcroft	1.1
4			#include "GAD_OPTIONS.h"
5
6			SUBROUTINE GAD_OS7MP_ADV_X(
7			I bi,bj,k,deltaTloc,
8			I uTrans, uFld,
9			I maskLocW, Q,
10			O uT,
11			I myThid )
12			C /==========================================================\
13			C \| SUBROUTINE GAD_OS7MP_ADV_X \|
14			C \| o Compute Zonal 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			_RL deltaTloc
27			_RL uTrans(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
28			_RL uFld (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
29			_RS maskLocW(1-OLx:sNx+OLx,1-OLy:sNy+OLy)
30			_RL Q (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
31			_RL uT (1-OLx:sNx+OLx,1-OLy:sNy+OLy)
32			INTEGER myThid
33
34			C == Local variables ==
35			INTEGER i,j
36			_RL cfl,Psi
37			_RL uLoc,Fac,Del,DelIp,DelI,Phi,Eps,rp1h,Msk
38			_RL Qippp,Qipp,Qip,Qi,Qim,Qimm,Qimmm
39			_RL MskIpp,MskIp,MskI,MskIm,MskImm,MskImmm
40			_RL d2,d2p1,d2m1,A,B,C,D
41			_RL dp1h,dm1h,qMD,qUL,qLC,PhiMD,PhiLC,PhiMin,PhiMax
42
43			Eps = 1. _d -20
44
45			DO j=1-Oly,sNy+Oly
46			uT(1-Olx,j)=0. _d 0
47			uT(2-Olx,j)=0. _d 0
48			uT(3-Olx,j)=0. _d 0
49			uT(4-Olx,j)=0. _d 0
50			uT(sNx+Olx-2,j)=0. _d 0
51			uT(sNx+Olx-1,j)=0. _d 0
52			uT(sNx+Olx,j)=0. _d 0
53			DO i=1-Olx+4,sNx+Olx-3
54
55			uLoc = uFld(i,j)
56			cfl = abs(uLocdeltaTlocrecip_dxC(i,j,bi,bj))
57
58			IF (uLoc.gt.0.) THEN
59			Qippp = Q(i+2,j)
60			Qipp = Q(i+1,j)
61			Qip = Q(i,j)
62			Qi = Q(i-1,j)
63			Qim = Q(i-2,j)
64			Qimm = Q(i-3,j)
65			Qimmm = Q(i-4,j)
66
67			MskIpp = maskLocW(i+2,j)
68			MskIp = maskLocW(i+1,j)
69			MskI = maskLocW(i,j)
70			MskIm = maskLocW(i-1,j)
71			MskImm = maskLocW(i-2,j)
72			MskImmm = maskLocW(i-3,j)
73			ELSEIF (uLoc.lt.0.) THEN
74			Qippp = Q(i-3,j)
75			Qipp = Q(i-2,j)
76			Qip = Q(i-1,j)
77			Qi = Q(i,j)
78			Qim = Q(i+1,j)
79			Qimm = Q(i+2,j)
80			Qimmm = Q(i+3,j)
81
82			MskIpp = maskLocW(i-2,j)
83			MskIp = maskLocW(i-1,j)
84			MskI = maskLocW(i,j)
85			MskIm = maskLocW(i+1,j)
86			MskImm = maskLocW(i+2,j)
87			MskImmm = maskLocW(i+3,j)
88			ENDIF
89
90			IF (uLoc.ne.0.) THEN
91			C 2nd order correction [i i-1]
92			Fac = 1.
93			Del = Qip-Qi
94			Msk = MskI
95			Phi = Msk * Fac * Del
96			C 3rd order correction [i i-1 i-2]
97			Fac = Fac * ( cfl + 1. )/3.
98			Del = Del - ( Qi-Qim )
99			Msk = Msk * MskIm
100			Phi = Phi - Msk * Fac * Del
101			C 4th order correction [i+1 i i-1 i-2]
102			Fac = Fac * ( cfl - 2. )/4.
103			Del = ( Qipp-2.*Qip+Qi ) - Del
104			Msk = Msk * MskIp
105			Phi = Phi + Msk * Fac * Del
106			C 5th order correction [i+1 i i-1 i-2 i-3]
107			Fac = Fac * ( cfl - 3. )/5.
108			Del = Del - ( Qip-3.Qi+3.Qim-Qimm )
109			Msk = Msk * MskImm
110			Phi = Phi + Msk * Fac * Del
111			C 6th order correction [i+2 i+1 i i-1 i-2 i-3]
112			Fac = Fac * ( cfl + 2. )/6.
113			Del = ( Qippp-4.Qipp+6.Qip-4.*Qi+Qim ) - Del
114			Msk = Msk * MskIpp
115			Phi = Phi + Msk * Fac * Del
116			C 7th order correction [i+2 i+1 i i-1 i-2 i-3 i-4]
117			Fac = Fac * ( cfl + 2. )/7.
118			Del = Del - ( Qipp-5.Qip+10.Qi-10.Qim+5.Qimm-Qimmm )
119			Msk = Msk * MskImmm
120			Phi = Phi - Msk * Fac * Del
121
122			DelIp = ( Qip - Qi ) * MskI
123	mlosch	1.2	Phi = sign(1. _d 0,Phi)*sign(1. _d 0,DelIp)
124			& *abs(Phi+Eps)/abs(DelIp+Eps)
125	adcroft	1.1
126			DelI = ( Qi - Qim ) * MskIm
127	mlosch	1.2	rp1h =sign(1. _d 0,DelI)*sign(1. _d 0,DelIp)
128			& *abs(DelI+Eps)/abs(DelIp+Eps)
129	adcroft	1.1
130			C TVD limiter
131	mlosch	1.2	! Phi = max(0. _d 0, min( 2./(1-cfl), Phi, 2.*rp1h/cfl ) )
132	adcroft	1.1
133			C MP limiter
134			d2 = ( ( Qip + Qim ) - 2.Qi ) MskI * MskIm
135			d2p1 = ( ( Qipp + Qi ) - 2.Qip ) MskIp * MskI
136			d2m1 = ( ( Qi + Qimm ) - 2.Qim ) MskIm * MskImm
137			A = 4.*d2 - d2p1
138			B = 4.*d2p1 - d2
139			C = d2
140			D = d2p1;
141	mlosch	1.2	dp1h = max(min(A,B,C,D),0. _d 0)+min(max(A,B,C,D),0. _d 0)
142	adcroft	1.1	A = 4.*d2m1 - d2
143			B = 4.*d2 - d2m1
144			C = d2m1
145			D = d2;
146	mlosch	1.2	dm1h = max(min(A,B,C,D),0. _d 0)+min(max(A,B,C,D),0. _d 0)
147	adcroft	1.1	qMD = 0.5*( ( Qi + Qip ) - dp1h )
148			qUL = Qi + (1.-cfl)/cfl*( Qi-Qim )
149			qLC = Qi + 0.5( 1.+dm1h/(Qi-Qim+Eps) )(qUL-Qi)
150			PhiMD = 2./(1.-cfl)*(qMD-Qi+Eps)/(Qip-Qi+Eps)
151			PhiLC = 2.rp1h/cfl(qLC-Qi+Eps)/(qUL-Qi+Eps)
152	mlosch	1.2	PhiMin = max(min(0. _d 0,PhiMD),
153			& min(0. _d 0,2.*rp1h/cfl,PhiLC))
154			PhiMax = min(max(2. _d 0/(1.-cfl),PhiMD),
155			& max(0. _d 0,2.*rp1h/cfl,PhiLC))
156	adcroft	1.1	Phi = max(PhiMin,min(Phi,PhiMax))
157
158			Psi = Phi * 0.5 * (1. - cfl)
159			uT(i,j) = uTrans(i,j)( Qi + PsiDelIp )
160			ELSE
161			uT(i,j) = 0.
162			ENDIF
163
164			ENDDO
165			ENDDO
166
167			RETURN
168			END