Consider the laminar flow of a viscous, incompressible fluid in a square cavity bounded by three stationary walls and a lid moving at a constant velocity in its own plane, as shown in Fig...

Consider the laminar flow of a viscous, incompressible fluid in a square cavity bounded by three stationary walls and a lid moving at a constant velocity in its own plane, as shown in Fig. 10.8.7. Singularities exist at each corner where the moving lid meets a fixed wall. This example is one that has been extensively studied by analytical, numerical, and experimental methods (see [200–202], for example), and it is often used as a benchmark problem to verify a computational scheme. Assuming a unit square (a = 1), the velocity of the top wall to be unity (v0 = 1), and using uniform meshes of (a) 8 × 8 linear elements and (b) 4 × 4 nine-node quadratic elements, determine the velocity and pressure fields. At the singular points, namely at the top corners of the lid, assume that vx(x, 1) = v0 = 1.0.