Page 217 - Computational Fluid Dynamics for Engineers

Problems 205

u
——J—W, m=—, 77=—, C = T
dx fj,
so that Eqs. (P6.1.1) and (P6.1.2) can be written as

du*{0,Q
= 0, «*(1,C) = 0 (P6.1.4a)
dr/
du*(j],0)
= 0, u*(»7,l) = 0 (P6.1.4b)

Compare your results with the analytical solution given by

where
X n£=(2n+1)^, n = 0,1,2,...
Take m — 2, zi?7 = zl£ = 0.002 and a convergence criterion of
+1) 10 7
max K^ - "Wl < " (P6.1.6)
i,j '-7 '-7
Note that Subroutine GAUSS (Table 4.2) remains unchanged. Note also the
subroutine POISSON requires changes given below,
SUBROUTINE P0ISS0N(II,JJ,TX,TY,F,U)
DIMENSION A(100,100),B(100,100),C(100,100),D(100,100),E(100,100)
DIMENSION DELTA(100,100,100), DELTT(100,100), BM(100,100)
DIMENSION DM(100,100),F(100,100),W(100,100),UT(100),U(100,100)
C ELEMENTS OF DIAGONAL VECTORS IN THE BLOCK MATRICES A,B AND C
DO 5 1=1,11
DO 5 J=1,JJ
A(I,J) = -TX
B(I,J) = 1.
C(I,J) = -TX
D(I,J) = -TY
E(I,J) = -TY
5 CONTINUE
DO 6 1=1,11
B(I,1) = l.-4./3.*TY
E(I,1) = -2./3.*TY
6 CONTINUE
DO 7 J=1,JJ
B(1,J) = B(l,J)-4./3.*TX
C(1,J) = -2./3.*TX
7 CONTINUE

The remaining statements in this subroutine are the same as those in Table 4.3
starting with