FIVOL算法语句 fortran
程序语句：PROGRAM FIVOL
DIMENSION X(21,21),Y(21,21),QAB(21,21),PAB(21,21),QBC(21,21),&
&PBC(21,21),QCD(21,21),PCD(21,21),QDA(21,21),PDA(21,21),&
&PHI(21,21),PHIX(21,21)
OPEN(1,FILE='FIVOL.DAT')
OPEN(6,FILE='FIVOL.OUT')
READ(1,1)JMAX,KMAX,NMAX
READ(1,2)RW,RX,RY,RZ,THEB,THEH,EPS,OM
1 FORMAT(8(I5))
2 FORMAT(8(E10.3))
WRITE(6,3)
WRITE(6,4)JMAX,KMAX,NMAX,EPS,OM
WRITE(6,5)RW,RX,RY,RZ,THEB,THEH
3 FORMAT('LAPLACE EQUATION BY FINITE VOLUME METHOD',//)
4 FORMAT('JMAX=',I2,'KMAX=',I2,'NMAX=',I5,&
&15X,'EPS=',E10.3,'OM=',F5.3)
5 FORMAT('RW=',F5.3,'RX=',F5.3,'RY=',F5.3,'RZ=',F5.3,&
&15X,'THEB=',F5.1,'THEN=',F5.1,//)
JMAP=JMAX-1
KMAP=KMAX-1
AJM=JMAP
AKM=KMAP
DRWX=(RX-RW)/AJM
DRZY=(RY-RZ)/AKM
DTH=(THEH-THEB)/AKM
PI=3.1415927
DO 7 K=1,KMAX
AK=K-1
THK=(THEB+AK*DTH)*PI/180.
CK=COS(THK)
SK=SIN(THK)
DR=DRWX+(DRZY-DRWX)*AK/AKM
RWZ=RW+(RZ-RW)*AK/AKM
DO 6 J=1,JMAX
AJ=J-1
R=RWZ+AJ*DR
X(J,K)=R*CK
Y(J,K)=R*SK
PHIX(J,K)=SK/R
PHI(J,K)=PHIX(J,K)
6 CONTINUE
7 CONTINUE
DO 8 J=1,JMAX
PHI(J,1)=0.
PHI(J,KMAX)=PHIX(J,KMAX)
8 CONTINUE
DO 9 K=1,KMAX
PHI(1,K)=PHIX(1,K)
PHI(JMAX,K)=PHIX(JMAX,K)
9 CONTINUE
DO 11 K=2,KMAP
KM=K-1
KP=K+1
DO 10 J=2,JMAP
JM=J-1
JP=J+1
XA=0.25*(X(J,K)+X(JM,K)+X(JM,KM)+X(J,KM))
YA=0.25*(Y(J,K)+Y(JM,K)+Y(JM,KM)+Y(J,KM))
XB=0.25*(X(J,K)+X(J,KM)+X(JP,KM)+X(JP,K))
YB=0.25*(Y(J,K)+Y(J,KM)+Y(JP,KM)+Y(JP,K))
XC=0.25*(X(J,K)+X(JP,K)+X(JP,KP)+X(J,KP))
YC=0.25*(Y(J,K)+Y(JP,K)+Y(JP,KP)+Y(J,KP))
XD=0.25*(X(J,K)+X(J,KP)+X(JM,KP)+X(JM,K))
YD=0.25*(Y(J,K)+Y(J,KP)+Y(JM,KP)+Y(JM,K))
DXA=XB-XA
DYA=YB-YA
DXK=X(J,K)-X(J,K-1)
DYK=Y(J,K)-Y(J,K-1)
SAB=ABS(DXA*DYK-DXK*DYA)
QAB(J,K)=(DXA*DXA+DYA*DYA)/SAB
PAB(J,K)=(DXA*DXK+DYA*DYK)/SAB
DXB=XC-XB
DYB=YC-YB
DXJ=X(J,K)-X(J+1,K)
DYJ=Y(J,K)-Y(J+1,K)
SBC=ABS(DYJ*DXB-DXJ*DYB)
QBC(J,K)=(DXB*DXB+DYB*DYB)/SBC
PBC(J,K)=(DXB*DXJ+DYB*DYJ)/SBC
DXC=XD-XC
DYC=YD-YC
DXK=X(J,K)-X(J,K+1)
DYK=Y(J,K)-Y(J,K+1)
SCD=ABS(DXC*DYK-DYC*DXK)
QCD(J,K)=(DXC*DXC+DYC*DYC)/SCD
PCD(J,K)=(DXC*DXK+DYC*DYK)/SCD
DXD=XA-XD
DYD=YA-YD
DXJ=X(J,K)-X(J-1,K)
DYJ=Y(J,K)-Y(J-1,K)
SDA=ABS(DXJ*DYD-DYJ*DXD)
QDA(J,K)=(DXD*DXD+DYD*DYD)/SDA
PDA(J,K)=(DXD*DXJ+DYD*DYJ)/SDA
10 CONTINUE
11 CONTINUE
DO 14 N=1,NMAX
SUM=0
DO 13 K=2,KMAP
KM=K-1
KP=K+1
DO 12 J=2,KMAP
JM=J-1
JP=J+1
PHD=0.25*(PCD(J,K)-PDA(J,K))*PHI(JM,KP)
PHD=PHD+(QCD(J,K)+0.25*(PBC(J,K)-PDA(J,K)))*PHI(J,KP)
PHD=PHD+0.25*(PBC(J,K)-PCD(J,K))*PHI(JP,KP)
PHD=PHD+(QDA(J,K)+0.25*(PCD(J,K)-PAB(J,K)))*PHI(JM,K)
PHD=PHD+(QBC(J,K)+0.25*(PAB(J,K)-PCD(J,K)))*PHI(JP,K)
PHD=PHD+0.25*(PDA(J,K)-PAB(J,K))*PHI(JM,KM)
PHD=PHD+(QAB(J,K)+0.25*(PDA(J,K)-PBC(J,K)))*PHI(J,KM)
PHD=PHD+0.25*(PAB(J,K)-PBC(J,K))*PHI(JP,KM)
PHD=PHD/(QAB(J,K)+QBC(J,K)+QCD(J,K)+QDA(J,K))
DIF=PHD-PHI(J,K)
SUM=SUM+DIF*DIF
PHI(J,K)=PHI(J,K)+OM*DIF
12 CONTINUE
13 CONTINUE
RMS=SQRT(SUM/(AJM-1.)/(AKM-1.))
IF(RMS.LT.EPS)GOTO 16
14 CONTINUE
WRITE(6,15)NMAX,RMS
15 FORMAT('CONVERGENCE NOT ACHIEVED IN',I5,'STEPS',5X,'RMS=',E12.5)
16 SUM=0.
DO 21 K=1,KMAX
WRITE(6,17)K
17 FORMAT(/,'K=',I2)
DO 18 J=1,JMAX
DIF=PHI(J,K)-PHIX(J,K)
SUM=SUM+DIF*DIF
18 CONTINUE
WRITE(6,19)(PHI(J,K),J=1,JMAX)
WRITE(6,20)(PHIX(J,K),J=1,JMAX)
19 FORMAT(' PHI=',10F7.4)
20 FORMAT(' PHIX=',10F7.4)
21 CONTINUE
RMS=SQRT(SUM/(AJM-1.)/(AKM-1.))
WRITE(6,22)N,RMS
22 FORMAT(/,'CONVERGED AFTER ',I3, ' STEPS',4X,' RMS=',E12.5)
STOP
END PROGRAM
运行结果：
LAPLACE EQUATION BY FINITE VOLUME METHOD
JMAX= 6KMAX= 6NMAX= 50 EPS= 0.100E-10OM=1.500
RW=0.100RX=1.000RY=1.000RZ=0.100 THEB= 0.0THEN= 90.0
CONVERGENCE NOT ACHIEVED IN 50STEPS RMS= 0.17568E-06
K= 1
PHI= 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
PHIX= 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
K= 2
PHI= 3.0902 1.2439 0.7445 0.5205 0.3929 0.3090
PHIX= 3.0902 1.1036 0.6718 0.4828 0.3769 0.3090
K= 3
PHI= 5.8779 2.3473 1.4036 0.9828 0.7441 0.5878
PHIX= 5.8779 2.0992 1.2778 0.9184 0.7168 0.5878
K= 4
PHI= 8.0902 3.1786 1.8990 1.3345 1.0163 0.8090
PHIX= 8.0902 2.8893 1.7587 1.2641 0.9866 0.8090
K= 5
PHI= 9.5106 3.6209 2.1680 1.5349 1.1802 0.9511
PHIX= 9.5106 3.3966 2.0675 1.4860 1.1598 0.9511
K= 6
PHI=10.0000 3.5714 2.1739 1.5625 1.2195 1.0000
PHIX=10.0000 3.5714 2.1739 1.5625 1.2195 1.0000
CONVERGED AFTER 51 STEPS RMS= 0.13258E+00
转自：http://blog.sina.com.cn/s/blog_a319f5ff0101jhth.html
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