pkg/generic_advdiff/gad_os7mp_adv_x.F

C $Header: $
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.,Phi)*sign(1.,DelIp)*abs(Phi+Eps)/abs(DelIp+Eps)

         DelI = ( Qi - Qim ) * MskIm
         rp1h =sign(1.,DelI)*sign(1.,DelIp)*abs(DelI+Eps)/abs(DelIp+Eps)

C        TVD limiter
!        Phi = max(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.)+min(max(A,B,C,D),0.)
         A = 4.*d2m1 - d2
         B = 4.*d2 - d2m1
         C = d2m1
         D = d2;
         dm1h = max(min(A,B,C,D),0.)+min(max(A,B,C,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.,PhiMD),min(0.,2.*rp1h/cfl,PhiLC))
         PhiMax = min(max(2./(1.-cfl),PhiMD),max(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	C $Header: $
2	C $Name: $
3
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	Phi = sign(1.,Phi)sign(1.,DelIp)abs(Phi+Eps)/abs(DelIp+Eps)
124
125	DelI = ( Qi - Qim ) * MskIm
126	rp1h =sign(1.,DelI)sign(1.,DelIp)abs(DelI+Eps)/abs(DelIp+Eps)
127
128	C TVD limiter
129	! Phi = max(0., min( 2./(1-cfl), Phi, 2.*rp1h/cfl ) )
130
131	C MP limiter
132	d2 = ( ( Qip + Qim ) - 2.Qi ) MskI * MskIm
133	d2p1 = ( ( Qipp + Qi ) - 2.Qip ) MskIp * MskI
134	d2m1 = ( ( Qi + Qimm ) - 2.Qim ) MskIm * MskImm
135	A = 4.*d2 - d2p1
136	B = 4.*d2p1 - d2
137	C = d2
138	D = d2p1;
139	dp1h = max(min(A,B,C,D),0.)+min(max(A,B,C,D),0.)
140	A = 4.*d2m1 - d2
141	B = 4.*d2 - d2m1
142	C = d2m1
143	D = d2;
144	dm1h = max(min(A,B,C,D),0.)+min(max(A,B,C,D),0.)
145	qMD = 0.5*( ( Qi + Qip ) - dp1h )
146	qUL = Qi + (1.-cfl)/cfl*( Qi-Qim )
147	qLC = Qi + 0.5( 1.+dm1h/(Qi-Qim+Eps) )(qUL-Qi)
148	PhiMD = 2./(1.-cfl)*(qMD-Qi+Eps)/(Qip-Qi+Eps)
149	PhiLC = 2.rp1h/cfl(qLC-Qi+Eps)/(qUL-Qi+Eps)
150	PhiMin = max(min(0.,PhiMD),min(0.,2.*rp1h/cfl,PhiLC))
151	PhiMax = min(max(2./(1.-cfl),PhiMD),max(0.,2.*rp1h/cfl,PhiLC))
152	Phi = max(PhiMin,min(Phi,PhiMax))
153
154	Psi = Phi * 0.5 * (1. - cfl)
155	uT(i,j) = uTrans(i,j)( Qi + PsiDelIp )
156	ELSE
157	uT(i,j) = 0.
158	ENDIF
159
160	ENDDO
161	ENDDO
162
163	RETURN
164	END