Page 282 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

SOME EXAMPLES OF FLUID FLOW AND HEAT TRANSFER PROBLEMS
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the first mesh (Figure 9.9 (a)), at different sections of the geometry, are compared with the
experimental data of Denham et al. (Denham and Patrik 1974).
The u 1 velocity contours (Figures 9.10(a) and (b)) are marked with the recirculation
pattern downstream of the step. This was the expected pattern in a problem of this nature.
The pressure contours are marked with minor oscillations, which was due to the unstructured
mesh used. The use of some form of artificial dissipation would eliminate these oscillations
but compromise the accuracy of the solution.
Double-driven cavity

As the name suggests, a double-driven cavity is different from the lid-driven cavity, dis-
cussed in the previous subsection, because of the way the double lids are used. In a
double-driven cavity, the lids are moved on both the top and the bottom sides of the cavity.
In order to study the effects of a double-driven action, the geometry shown in Figure 9.11(a)

u 1 = 1, u 2 = 0

u 1 = u 2 = 0

L

0.4L
u 1 = u 2 = 0

u 1 = −1, u 2 = 0
L 0.4L
(a) Geometry and boundary conditions

(b) Uniform unstructured mesh, Nodes:18,717, elements:36,834
Figure 9.11 Incompressible isothermal flow in a double-driven cavity. Geometry and mesh