Page 370 - Computational Fluid Dynamics for Engineers

12.5 Finite Volume Method 361

The coefficients of the damping terms ei and e e are usually selected according
to
0<e e< (12.4.24a)
8(1+0
and
2e e (12.4.24b)
to ensure stability and optimal convergence rate [2].

12.5 Finite Volume Method

In this section, we discuss the application of the finite volume of Section 5.6 to
two dimensional compressible flows given by Eq. (2.2.30)

(12.5.1)
dt W j dx dy Re\dx dy

with Q, E, F, E v and F v given by Eqs. (2.2.32) and (2.2.33). The method has
been extensively developed by Jameson [4].
We first integrate (12.5.1) over rectangular cell f2{j (see Fig. 12.2).

The left-hand-side becomes
dQ 9Qi tj dQjj AxAy
Qi
-dt dxdy = -dT 'i dt (12.5.2a)

while the right-hand-side is expanded as

Av • unknown
*-*r- x y x boundary
yj

a Ax

yi t • Fig. 12.2. Subdomains f2ij, in-
* - * x x terior (unknown) and boundary
y 0
points.