214
7. Solution of the Navier-Stokes Equations
- e- - Staggered
-oColocated
1200
1 equations three orders of magnitude, as a
0.5 0.6 0.7 0.8 0.9 1.0 function of the under-relaxation factor a,
(lid-driven cavity flow at Re = 1000)
Fig. 7.15. Numbers of outer iterations
required to reduce the residual level in all
was evaluated using the expression (7.149). It is 0.5% on the 8 x 8 CV grid
and 0.002% on the 128 x 128 CV grid. These differences are two orders of
magnitude smaller than the discretization errors on corresponding grids (53%
and 0.4010, respectively) and can be neglected.
Fig. 7.16. Velocity vectors in
buoyancy-driven cavity flow at the
Rayleigh number R a = lo5 and
Prandtl number Pr = 0.1
We next consider 2D buoyancy-driven flow in a square cavity as shown in
Figs. 7.16 and 7.17. The cold and hot walls are isothermal. The heated fluid
is rising along the hot wall, while cooled fluid is falling along the cold wall.
The Prandtl number is 0.1, and the temperature difference and other fluid
properties are chosen such that the Rayleigh number is