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*DECK TRIDCO
SUBROUTINE TRIDCO (IELEM,IR,NEL,K,VOL0,MAT,DIF,DDF,XX,YY,ZZ,DD,KN,
1 QFR,CYLIND,IPR,A)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Compute the derivative or variation of mesh centered finite difference
* coefficients in element K.
*
*Copyright:
* Copyright (C) 2002 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s): A. Hebert
*
*Parameters: input
* IELEM degree of the polynomial basis: =1 (linear/finite
* differences); =2 (parabolic); =3 (cubic); =4 (quartic).
* IR first dimension of matrix DIF.
* NEL total number of finite elements.
* K index of finite element under consideration.
* VOL0 volume of finite element under consideration.
* MAT mixture index assigned to each element.
* DIF directional diffusion coefficients
* DDF derivative or variation of directional diffusion coefficients.
* XX X-directed mesh spacings.
* YY Y-directed mesh spacings.
* ZZ Z-directed mesh spacings.
* DD used with cylindrical geometry.
* KN element-ordered unknown list:
* .GT.0: neighbour index;
* =-1: void/albedo boundary condition;
* =-2: reflection boundary condition;
* =-3: ZERO flux boundary condition;
* =-4: SYME boundary condition (axial symmetry).
* QFR element-ordered boundary conditions.
* CYLIND cylindrical geometry flag (set with CYLIND =.true.).
* IPR type of coefficient calculation:
* .eq.1 take derivative of MCFD coefficients;
* .ge.2 take variation of MCFD coefficients.
*
*Parameters: output
* A derivative or variation of mesh centered finite difference
* coefficients.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER IELEM,IR,NEL,K,MAT(NEL),KN(6),IPR
REAL VOL0,DIF(IR,3),DDF(IR,3),XX(NEL),YY(NEL),ZZ(NEL),DD(NEL),
1 QFR(6)
LOGICAL CYLIND
DOUBLE PRECISION A(6)
*----
* LOCAL VARIABLES
*----
DOUBLE PRECISION VHARM,DHARM,DIN,DOT
*
* VARIATION FORMULA:
VHARM(X1,X2,DIF1,DIF2,DDF1,DDF2)=2.0D0*((DIF1+DDF1)*(DIF2+DDF2)
1 /(X1*(DIF2+DDF2)+X2*(DIF1+DDF1))-DIF1*DIF2/(X1*DIF2+X2*DIF1))
* DERIVATIVE FORMULA:
DHARM(X1,X2,DIF1,DIF2,DDF1,DDF2)=2.0D0*(X1*DIF2*DIF2*DDF1+
1 X2*DIF1*DIF1*DDF2)/(X1*DIF2+X2*DIF1)**2
*
DENOM=REAL((IELEM+1)*IELEM)
L=MAT(K)
DX=XX(K)
DY=YY(K)
DZ=ZZ(K)
IF(CYLIND) THEN
DIN=1.0D0-0.5D0*DX/DD(K)
DOT=1.0D0+0.5D0*DX/DD(K)
ELSE
DIN=1.0D0
DOT=1.0D0
ENDIF
KK1=KN(1)
KK2=KN(2)
KK3=KN(3)
KK4=KN(4)
KK5=KN(5)
KK6=KN(6)
IF(IPR.EQ.1) THEN
* DERIVATIVE FORMULA.
* X- SIDE:
IF(KK1.GT.0) THEN
A(1)=DHARM(DX,XX(KK1),DIF(L,1),DIF(MAT(KK1),1),DDF(L,1),
1 DDF(MAT(KK1),1))*DIN*VOL0/DX
ELSE IF(KK1.EQ.-1) THEN
A(1)=DHARM(DX,DX,DIF(L,1),DX*QFR(1)/DENOM,DDF(L,1),0.0)
1 *DIN*VOL0/DX
ELSE IF(KK1.EQ.-2) THEN
A(1)=0.0D0
ELSE IF(KK1.EQ.-3) THEN
A(1)=2.0D0*DDF(L,1)*DIN*VOL0/(DX*DX)
ENDIF
* X+ SIDE:
IF(KK2.GT.0) THEN
A(2)=DHARM(DX,XX(KK2),DIF(L,1),DIF(MAT(KK2),1),DDF(L,1),
1 DDF(MAT(KK2),1))*DOT*VOL0/DX
ELSE IF(KK2.EQ.-1) THEN
A(2)=DHARM(DX,DX,DIF(L,1),DX*QFR(2)/DENOM,DDF(L,1),0.0)
1 *DOT*VOL0/DX
ELSE IF(KK2.EQ.-2) THEN
A(2)=0.0D0
ELSE IF(KK2.EQ.-3) THEN
A(2)=2.0D0*DDF(L,1)*DOT*VOL0/(DX*DX)
ELSE IF(KK2.EQ.-4) THEN
IF(KK1.EQ.-4) CALL XABORT('TRIDCO: INCONSISTENT SYME (1).')
A(2)=A(1)
ENDIF
IF(KK1.EQ.-4) THEN
IF(KK2.EQ.-4) CALL XABORT('TRIDCO: INCONSISTENT SYME (2).')
A(1)=A(2)
ENDIF
* Y- SIDE:
IF(KK3.GT.0) THEN
A(3)=DHARM(DY,YY(KK3),DIF(L,2),DIF(MAT(KK3),2),DDF(L,2),
1 DDF(MAT(KK3),2))*VOL0/DY
ELSE IF(KK3.EQ.-1) THEN
A(3)=DHARM(DY,DY,DIF(L,2),DY*QFR(3)/DENOM,DDF(L,2),0.0)
1 *VOL0/DY
ELSE IF(KK3.EQ.-2) THEN
A(3)=0.0D0
ELSE IF(KK3.EQ.-3) THEN
A(3)=2.0D0*DDF(L,2)*VOL0/(DY*DY)
ENDIF
* Y+ SIDE:
IF(KK4.GT.0) THEN
A(4)=DHARM(DY,YY(KK4),DIF(L,2),DIF(MAT(KK4),2),DDF(L,2),
1 DDF(MAT(KK4),2))*VOL0/DY
ELSE IF(KK4.EQ.-1) THEN
A(4)=DHARM(DY,DY,DIF(L,2),DY*QFR(4)/DENOM,DDF(L,2),0.0)
1 *VOL0/DY
ELSE IF(KK4.EQ.-2) THEN
A(4)=0.0D0
ELSE IF(KK4.EQ.-3) THEN
A(4)=2.0D0*DDF(L,2)*VOL0/(DY*DY)
ELSE IF(KK4.EQ.-4) THEN
IF(KK3.EQ.-4) CALL XABORT('TRIDCO: INCONSISTENT SYME (3).')
A(4)=A(3)
ENDIF
IF(KK3.EQ.-4) THEN
IF(KK4.EQ.-4) CALL XABORT('TRIDCO: INCONSISTENT SYME (4).')
A(3)=A(4)
ENDIF
* Z- SIDE:
IF(KK5.GT.0) THEN
A(5)=DHARM(DZ,ZZ(KK5),DIF(L,3),DIF(MAT(KK5),3),DDF(L,3),
1 DDF(MAT(KK5),3))*VOL0/DZ
ELSE IF(KK5.EQ.-1) THEN
A(5)=DHARM(DZ,DZ,DIF(L,3),DZ*QFR(5)/DENOM,DDF(L,3),0.0)
1 *VOL0/DZ
ELSE IF(KK5.EQ.-2) THEN
A(5)=0.0D0
ELSE IF(KK5.EQ.-3) THEN
A(5)=2.0D0*DDF(L,3)*VOL0/(DZ*DZ)
ENDIF
* Z+ SIDE:
IF(KK6.GT.0) THEN
A(6)=DHARM(DZ,ZZ(KK6),DIF(L,3),DIF(MAT(KK6),3),DDF(L,3),
1 DDF(MAT(KK6),3))*VOL0/DZ
ELSE IF(KK6.EQ.-1) THEN
A(6)=DHARM(DZ,DZ,DIF(L,3),DZ*QFR(6)/DENOM,DDF(L,3),0.0)
1 *VOL0/DZ
ELSE IF(KK6.EQ.-2) THEN
A(6)=0.0D0
ELSE IF(KK6.EQ.-3) THEN
A(6)=2.0D0*DDF(L,3)*VOL0/(DZ*DZ)
ELSE IF(KK6.EQ.-4) THEN
IF(KK5.EQ.-4) CALL XABORT('TRIDCO: INCONSISTENT SYME (5).')
A(6)=A(5)
ENDIF
IF(KK5.EQ.-4) THEN
IF(KK6.EQ.-4) CALL XABORT('TRIDCO: INCONSISTENT SYME (6).')
A(5)=A(6)
ENDIF
ELSE
* VARIATION FORMULA.
* X- SIDE:
IF(KK1.GT.0) THEN
A(1)=VHARM(DX,XX(KK1),DIF(L,1),DIF(MAT(KK1),1),DDF(L,1),
1 DDF(MAT(KK1),1))*DIN*VOL0/DX
ELSE IF(KK1.EQ.-1) THEN
A(1)=VHARM(DX,DX,DIF(L,1),DX*QFR(1)/DENOM,DDF(L,1),0.0)
1 *DIN*VOL0/DX
ELSE IF(KK1.EQ.-2) THEN
A(1)=0.0D0
ELSE IF(KK1.EQ.-3) THEN
A(1)=2.0D0*DDF(L,1)*DIN*VOL0/(DX*DX)
ENDIF
* X+ SIDE:
IF(KK2.GT.0) THEN
A(2)=VHARM(DX,XX(KK2),DIF(L,1),DIF(MAT(KK2),1),DDF(L,1),
1 DDF(MAT(KK2),1))*DOT*VOL0/DX
ELSE IF(KK2.EQ.-1) THEN
A(2)=VHARM(DX,DX,DIF(L,1),DX*QFR(2)/DENOM,DDF(L,1),0.0)
1 *DOT*VOL0/DX
ELSE IF(KK2.EQ.-2) THEN
A(2)=0.0D0
ELSE IF(KK2.EQ.-3) THEN
A(2)=2.0D0*DDF(L,1)*DOT*VOL0/(DX*DX)
ELSE IF(KK2.EQ.-4) THEN
IF(KK1.EQ.-4) CALL XABORT('TRIDCO: INCONSISTENT SYME (7).')
A(2)=A(1)
ENDIF
IF(KK1.EQ.-4) THEN
IF(KK2.EQ.-4) CALL XABORT('TRIDCO: INCONSISTENT SYME (8).')
A(1)=A(2)
ENDIF
* Y- SIDE:
IF(KK3.GT.0) THEN
A(3)=VHARM(DY,YY(KK3),DIF(L,2),DIF(MAT(KK3),2),DDF(L,2),
1 DDF(MAT(KK3),2))*VOL0/DY
ELSE IF(KK3.EQ.-1) THEN
A(3)=VHARM(DY,DY,DIF(L,2),DY*QFR(3)/DENOM,DDF(L,2),0.0)
1 *VOL0/DY
ELSE IF(KK3.EQ.-2) THEN
A(3)=0.0D0
ELSE IF(KK3.EQ.-3) THEN
A(3)=2.0D0*DDF(L,2)*VOL0/(DY*DY)
ENDIF
* Y+ SIDE:
IF(KK4.GT.0) THEN
A(4)=VHARM(DY,YY(KK4),DIF(L,2),DIF(MAT(KK4),2),DDF(L,2),
1 DDF(MAT(KK4),2))*VOL0/DY
ELSE IF(KK4.EQ.-1) THEN
A(4)=VHARM(DY,DY,DIF(L,2),DY*QFR(4)/DENOM,DDF(L,2),0.0)
1 *VOL0/DY
ELSE IF(KK4.EQ.-2) THEN
A(4)=0.0D0
ELSE IF(KK4.EQ.-3) THEN
A(4)=2.0D0*DDF(L,2)*VOL0/(DY*DY)
ELSE IF(KK4.EQ.-4) THEN
IF(KK3.EQ.-4) CALL XABORT('TRIDCO: INCONSISTENT SYME (9).')
A(4)=A(3)
ENDIF
IF(KK3.EQ.-4) THEN
IF(KK4.EQ.-4) CALL XABORT('TRIDCO: INCONSISTENT SYME (10).')
A(3)=A(4)
ENDIF
* Z- SIDE:
IF(KK5.GT.0) THEN
A(5)=VHARM(DZ,ZZ(KK5),DIF(L,3),DIF(MAT(KK5),3),DDF(L,3),
1 DDF(MAT(KK5),3))*VOL0/DZ
ELSE IF(KK5.EQ.-1) THEN
A(5)=VHARM(DZ,DZ,DIF(L,3),DZ*QFR(5)/DENOM,DDF(L,3),0.0)
1 *VOL0/DZ
ELSE IF(KK5.EQ.-2) THEN
A(5)=0.0D0
ELSE IF(KK5.EQ.-3) THEN
A(5)=2.0D0*DDF(L,3)*VOL0/(DZ*DZ)
ENDIF
* Z+ SIDE:
IF(KK6.GT.0) THEN
A(6)=VHARM(DZ,ZZ(KK6),DIF(L,3),DIF(MAT(KK6),3),DDF(L,3),
1 DDF(MAT(KK6),3))*VOL0/DZ
ELSE IF(KK6.EQ.-1) THEN
A(6)=VHARM(DZ,DZ,DIF(L,3),DZ*QFR(6)/DENOM,DDF(L,3),0.0)
1 *VOL0/DZ
ELSE IF(KK6.EQ.-2) THEN
A(6)=0.0D0
ELSE IF(KK6.EQ.-3) THEN
A(6)=2.0D0*DDF(L,3)*VOL0/(DZ*DZ)
ELSE IF(KK6.EQ.-4) THEN
IF(KK5.EQ.-4) CALL XABORT('TRIDCO: INCONSISTENT SYME (11).')
A(6)=A(5)
ENDIF
IF(KK5.EQ.-4) THEN
IF(KK6.EQ.-4) CALL XABORT('TRIDCO: INCONSISTENT SYME (12).')
A(5)=A(6)
ENDIF
ENDIF
RETURN
END
|
