Page 278 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

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0.8
0.8 1 SOME EXAMPLES OF FLUID FLOW AND HEAT TRANSFER PROBLEMS
Vertical distance 0.6 Ghia et al. Vertical distance 0.6 Ghia et al.
Mesh1
Mesh2
0.4
0.4
0.2 0.2
0 0
−1 −0.5 0 0.5 1 −1 −0.5 0 0.5 1
Horizontal velocity Horizontal velocity
(a) Mesh1 (b) Mesh2
1 1

0.8 0.8
Vertical distance 0.6 Ghia et al. Vertical distance 0.6 Ghia et al.
Mesh4
Mesh3
0.4
0.4
0.2 0.2
0 0
−0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
Horizontal velocity Horizontal velocity
(c) Mesh3 (d) Mesh4

1 1
0.8 0.8
Vertical distance 0.6 Ghia et al. Vertical distance 0.6 Ghia et al.
Mesh6
Mesh5
0.4
0.4
0.2 0.2

0 0
−0.4 −0.2 0 0.2 0.4 0.6 0.8 1 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
Horizontal velocity Horizontal velocity
(e) Mesh5 (f) Mesh6
Figure 9.5 Incompressible isothermal flow in a lid-driven cavity. u 1 velocity profile along
the mid-vertical line. Comparison with the benchmark steady state results of Ghia et al.
(Ghia et al. 1982)

Flow past a backward-facing step
The lid-driven cavity problem considered in the previous subsection was a good example
of flow inside an enclosed area. It is therefore appropriate to consider a problem in which
the fluid is allowed to enter from an inlet section and exit from an outlet section. A typical
case of such an example is the flow past a backward-facing step, which is widely employed