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! version 3; Last Modified: May 7, 2008.
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***S/P LIN_DIFF_VERT1_TL TLM of LIN_DIFF_VERT1
*
SUBROUTINE LIN_DIFF_VERT1_TL(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,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)
REAL BETA5(N)
*
*
*Author
* S. Laroche (fev 2001)
*
*Revisions
* 001 L. Spacek (Jun 2008) - Staggered version
*
*Object
* to solve a TLM vertical diffusion equation by finite
* differences
*
*Arguments
*
**
*
**
*
INTEGER I, K
REAL SC, SCTU, ST, SB, HM, HP, HD, KUM, KUP, SCK1
EXTERNAL LIN_DIFUVD1_TL, LIN_DIFUVD2_TL
*
*
******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
*
*
* (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
*
******END TRAJECTORY ************************************************
*
*
* (1) CONSTRUIRE L'OPERATEUR TRIDIAGONAL DE DIFFUSION N=(A,B,C)
* ET LE TERME CONTRE-GRADIENT (DANS D)
*
*
* 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)
A(I,1) = 0.
B(I,1) = -SCK1* KU(I,1)/(HP*HD)
C(I,1) = SCK1*SCK1*KU(I,1)/(HP*HD)
D(I,1) = SCK1* KU(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)
A(I,K) = KU(I,K-1)/(HM*HD)
B(I,K) = -KU(I,K-1)/(HM*HD) - KU(I,K)/(HP*HD)
C(I,K) = KU(I,K)/(HP*HD)
D(I,K) = KU(I,K)*GU(I,K)/HD - KU(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)
A(I,NK) = KU(I,NK-1)/(HM*HD)
B(I,NK) = -KU(I,NK-1)/(HM*HD)
C(I,NK) = 0.
D(I,NK) = -KU(I,NK-1)*GU(I,NK-1)/HD
ENDDO
*
*
* (2) CALCULER LE COTE DROIT D=TAU*(SC*N(U)+R+D/DS(KU*GU))
*
CALL LIN_DIFUVD1_TL (D, SC, A, B, C, U, D, N, NK,
& A5, B5, C5, U5)
DO K=1,NK
DO I=1,N
D(I,K) = TAU*D(I,K)
ENDDO
ENDDO
*
* (3) CALCULER OPERATEUR DU COTE GAUCHE
*
DO K=1,NK
DO I=1,N
A(I,K) = - SC*TAU*A(I,K)
B(I,K) = - SC*TAU*B(I,K)
C(I,K) = - SC*TAU*C(I,K)
A5(I,K) = - SC*TAU*A5(I,K)
B5(I,K) = 1.0 - SC*TAU*B5(I,K)
C5(I,K) = - SC*TAU*C5(I,K)
ENDDO
ENDDO
*
* (4) AJOUTER TERME DE FLUX DE SURFACE POUR TYPE='U'/'UT'
*
DO I=1,N
HD=SB(I)-SK(I,NK-1)
B5(I,NK) = B5(I,NK) - SC*TAU*BETA5(I)/HD
B(I,NK) = B(I,NK) - SC*TAU*BETA(I)/HD
D(I,NK) = D(I,NK) + (ALFA(I)+BETA5(I)*U(I,NK))*TAU/HD
& + (BETA(I)*U5(I,NK))*TAU/HD
ENDDO
*
* (5) RESOUDRE SYSTEME TRIDIAGONAL [A,B,C] X = D. METTRE X DANS TU.
*
CALL LIN_DIFUVD2_TL (TU, A, B, C, D, D, N, NK,
& A5, B5, C5, D5, W1, W2, W3)
*
* (6) OBTENIR TENDANCE
*
DO K=1,NK
DO I=1,N
TU(I,K)=TU(I,K)/TAU
ENDDO
ENDDO
*
RETURN
END