Page 348 - Computational Fluid Dynamics for Engineers

338 11. Incompressible Navier-Stokes Equations

f 0 Vj <H -h
u (11.5.5a)
0,j = < yj-H + h (yj-H + h^ 2 1
1.5 H -h<yj <H
h h

v 0j = 0 (11.5.5b)
poj = 2pij - p2j (11.5.5c)

No-slip surface:
At y = 0 and 0 < i < I,
v>i,o = Vi to = 0 (11.5.6a)

and the pressure is approximated with second-order accurate extrapolation
Pi,o = 2pi,i Pi,2 (11.5.6b)
-
Symmetry line:
At the centerline, j = J, 0 < i < , ^ and ^ are represented by second order
/
approximations
UiJ (11.5.7a)

4pi,j-i ~Pi,j-2
PiJ (11.5.7b)
In addition, we set
VLJ = 0 (11.5.7c)
Outflow:
The boundary conditions a t i = 7 , 0 < j < J are written as

(11.5.8a)
2
Pi J = P / - i j -PI-2J (11.5.8b)
vi J = vi-ij (11.5.8c)

11.5.2 Initial Conditions

The initial conditions are:

u(x, y, 0) = v(x, y, 0) = p(x, y, 0) = 0 (11.5.9)
Here we assume that at the i = 0 boundary, uoj is given by Eq. (11.5.5a)
and at i = , u / j is given by
/

u / j = 1.5A (11.5.10)