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***S/P LIN_DIFF_VERT1_AD ADJ of LIN_DIFF_VERT1
*
SUBROUTINE LIN_DIFF_VERT1_AD(TU, U, KU, GU, ALFA, BETA, S, SK, 2,3
% TAU, F, A, B, C, D, N, NK,
% U5,KU5,A5,B5,C5,D5,W1,W2,W3,W4,BETA5)
*
#include "impnone.cdk"
INTEGER N, NK
REAL TU(N, NK), U(N, NK), KU(N, NK), GU(N, NK)
REAL ALFA(N), BETA(N), S(N,NK), SK(N,NK), TAU, F
REAL A(N, NK), B(N, NK), C(N, NK), D(N, NK)
REAL U5(N, NK), KU5(N, NK)
REAL A5(N, NK), B5(N, NK), C5(N, NK), D5(N, NK)
REAL W1(N, NK), W2(N, NK), W3(N, NK), W4(N, NK)
REAL BETA5(N)
*
*Author
* S. Laroche (oct 2000)
*
*Revisions
* 001 M. Tanguay - Preserve trajectory for LIN_DIFUVD1_AD
* 002 L. Spacek (Jun 2008) - Staggered version
*
*Object
* adjoint of the vertical diffusion equation by finite
* differences
*
*Arguments
*
**
*
**
*
INTEGER I, K
REAL SC, SCTU, ST, SB, HM, HP, HD, KUM, KUP, SCK1
EXTERNAL LIN_DIFUVD1_AD, LIN_DIFUVD2_AD
*
REAL A5_1(N, NK), B5_1(N, NK), C5_1(N, NK)
*
******START TRAJECTORY **********************************************
*
ST(i)=S(i,1)-0.5*(S(i,2)-S(i,1))
SB(i)=1.
*
SC = 1.0
SCTU = 0
SCK1 = 0
*
*
* K=1
*
HM=0
DO I=1,N
HP=S(I,2)-S(I,1)
HD=0.5*(S(I,1)+S(I,2))-ST(I)
A5(I,1)=0
B5(I,1)=-SCK1*KU5(I,1)/(HP*HD)
C5(I,1)=-SCK1*B5(I,1)
D5(I,1)=SCK1*KU5(I,1)*GU(I,1)/HD
ENDDO
*
* K=2...NK-1
*
DO K=2,NK-1,1
DO I=1,N
HM=S(I,K)-S(I,K-1)
HP=S(I,K+1)-S(I,K)
HD=0.5*(HM+HP)
A5(I,K)=KU5(I,K-1)/(HM*HD)
B5(I,K)=-(KU5(I,K-1)/HM +KU5(I,K)/HP)/HD
C5(I,K)=KU5(I,K)/(HP*HD)
D5(I,K)=(KU5(I,K)*GU(I,K)-KU5(I,K-1)*GU(I,K-1))/HD
ENDDO
ENDDO
*
* K=NK
*
HP=0
DO I=1,N
HM=S(I,NK)-S(I,NK-1)
HD=SB(I)-SK(I,NK-1)
A5(I,NK)=KU5(I,NK-1)/(HM*HD)
B5(I,NK)=-(KU5(I,NK-1)/HM + 0)/HD
C5(I,NK)=0.
D5(I,NK)=(0-KU5(I,NK-1)*GU(I,NK-1))/HD
ENDDO
*
DO K=1,NK
DO I=1,N
A5_1(I,K) = A5(I,K)
B5_1(I,K) = B5(I,K)
C5_1(I,K) = C5(I,K)
ENDDO
ENDDO
*
*
* (2) CALCULER LE COTE DROIT D=TAU*(SC*N(U)+D/DS(KU*GU))
*
CALL LIN_DIFUVD1 (D5, SC, A5, B5, C5, U5, D5, N, NK)
DO K=1,NK
DO I=1,N
D5(I,K) = TAU*D5(I,K)
ENDDO
ENDDO
DO K=1,NK
DO I=1,N
A5(I,K) = - TAU*A5(I,K)
B5(I,K) = 1.0 - TAU*B5(I,K)
C5(I,K) = - TAU*C5(I,K)
ENDDO
ENDDO
DO I=1,N
HD=SB(I)-SK(I,NK-1)
B5(I,NK) = B5(I,NK) - SC*TAU*BETA5(I)/HD
ENDDO
*
* zeroing some adjoint variables
*
DO K=1,NK
DO I=1,N
A(I,K) = 0.0
B(I,K) = 0.0
C(I,K) = 0.0
D(I,K) = 0.0
W1(I,K) = 0.0
W2(I,K) = 0.0
W3(I,K) = 0.0
W4(I,K) = 0.0
ENDDO
ENDDO
*
******END TRAJECTORY ************************************************
*
*
* (6) OBTENIR TENDANCE
*
DO K=1,NK
DO I=1,N
TU(I,K)=TU(I,K)/TAU
ENDDO
ENDDO
*
* (5) RESOUDRE SYSTEME TRIDIAGONAL [A,B,C] X = D. METTRE X DANS TU.
*
CALL LIN_DIFUVD2_AD (TU, A, B, C, D, W4, N, NK,
& A5, B5, C5, D5, W1, W2, W3)
*
* (3) CALCULER OPERATEUR DU COTE GAUCHE
*
DO I=1,N
HD=SB(I)-SK(I,NK-1)
ALFA(I) = D(I,NK)*TAU/HD + ALFA(I)
BETA(I) = D(I,NK)*U5(I,NK)*TAU/HD + BETA(I)
U(I,NK) = D(I,NK)*BETA5(I)*TAU/HD + U(I,NK)
BETA(I) = - SC*TAU*B(I,NK)/HD + BETA(I)
ENDDO
*
DO K=1,NK
DO I=1,N
A(I,K) = - TAU*A(I,K)
B(I,K) = - TAU*B(I,K)
C(I,K) = - TAU*C(I,K)
ENDDO
ENDDO
*
*
* (2) CALCULER LE COTE DROIT D=TAU*(SC*N(U)+R+D/DS(KU*GU))
*
DO I=1,N
HD=SB(I)-SK(I,NK-1)
B5(I,NK) = B5(I,NK) + SC*TAU*BETA5(I)/HD
ENDDO
*
DO K=1,NK
DO I=1,N
A5(I,K) = - A5(I,K)/TAU
B5(I,K) = (1.0 - B5(I,K))/TAU
C5(I,K) = - C5(I,K)/TAU
D5(I,K) = TAU*D(I,K)
D(I,K) = 0.0
ENDDO
ENDDO
*
CALL LIN_DIFUVD1_AD (D5, SC, A, B, C, U, D, N, NK,
& A5_1, B5_1, C5_1, U5)
if(.false.) then
*
* (1) CONSTRUIRE L'OPERATEUR TRIDIAGONAL DE DIFFUSION N=(A,B,C)
* ET LE TERME CONTRE-GRADIENT (DANS D)
*
HP=0
DO I=1,N
HM=S(I,NK)-S(I,NK-1)
HD=SB(I)-0.5*(S(I,NK-1)+S(I,NK))
KU(I,NK-1) = -D(I,NK)*GU(I,NK-1)/HD + KU(I,NK-1)
KU(I,NK-1) = -B(I,NK)/(HM*HD) + KU(I,NK-1)
KU(I,NK-1) = A(I,NK)/(HM*HD) + KU(I,NK-1)
ENDDO
*
* K=2...NK-1
*
DO K=NK-1,2,-1
DO I=1,N
HM=S(I,K)-S(I,K-1)
HP=S(I,K+1)-S(I,K)
HD=0.5*(HM+HP)
KU(I,K) = D(I,K)*GU(I,K)/HD + KU(I,K)
KU(I,K-1) = -D(I,K)*GU(I,K-1)/HD + KU(I,K-1)
KU(I,K) = C(I,K)/(HP*HD) + KU(I,K)
KU(I,K-1) = -B(I,K)/(HM*HD) + KU(I,K-1)
KU(I,K) = -B(I,K)/(HP*HD) + KU(I,K)
KU(I,K-1) = A(I,K)/(HM*HD) + KU(I,K-1)
ENDDO
ENDDO
*
* K=1
*
HM=0
DO I=1,N
HP=S(I,2)-S(I,1)
HD=0.5*(S(I,1)+S(I,2))-ST(I)
KU(I,1) = SCK1*D(I,1)*GU(I,1)/HD + KU(I,1)
KU(I,1) = SCK1*SCK1*C(I,1)/(HP*HD) + KU(I,1)
KU(I,1) =-SCK1*B(I,1)/(HP*HD) + KU(I,1)
ENDDO
*
*
endif
RETURN
END