Page 378 - Computational Fluid Dynamics for Engineers

Appendix 12A 369

gu q 2
2 I g|M + 7-i)[?4-5(giM+ 9iM)]
(
QU + P
E =
guv 92 <73/9i
L{E t+p)u\ [{q 4 + (7 - 1)[94 - ^(92/91 + 9|/9i)]}92/gi J , J 2 A ^
^ 1 [ 93 n
g m ; 9293/^1
F =
2
^ + P 93M + (7 1 ) [ 9 4 - 5(92/9i+9i/9l)]
-
L(^t +p)u J L{94 + (7 - 1)[94 - 5(92/91 + 9l/9l)]}93/9i
The Jacobian matrices of convective terms are obtained by differenting E and
F respect to Q.

1 0 0
^ 2 + ^ 2 (3 - 7)u (1 — 7)1; 7 — 1
u 0
2
2
" 7 ^ + (7 - l)u(u 2 + v ) 7 ^ - { -^(3u 2 + v ) - ( 7 - l)uv 7u
0 0 1 0
—m; v ix 0
B
2
dQ ^M + ^ ^ V — (7 — \)u —(7 — 3)v 7 — 1
( 7 _ 1 ) V ( M 2 ^ _ yE± _ trzil( u2 3t; 2)
_ 7£r» + + _ ( 7 ^ u v + 7 V
(12A.2)
Similarly, the Jacobian matrices P, R, R x, M,N and N y are obtained from

'dVi'
[^] + tfx] =
d( Q dx .9Q X.
n 0 0
u 0 0
Vx ~\
[P] + [Rx] =
1 0
2
2
L (I -1?> - (i - i?> - & f (I - )* a - &)v £.
-
£
(12A.3)
dVi
[R]
dQ x
0 0 0
(12A.4)
4* 0 0
[R] l*
1 0
2
£
-(I - £W - (i - £)« - f (! - £)* (i - £)* £ J