Consider the lid-driven cavity problem of Example XXXXXXXXXXfor nonlinear analysis (i.e. solve Navier–Stokes equations for Re > 0). For the problem at hand, the Reynolds number (Re = ρv0a/µ) can be...

Consider the lid-driven cavity problem of Example 10.8.3 for nonlinear analysis (i.e. solve Navier–Stokes equations for Re > 0). For the problem at hand, the Reynolds number (Re = ρv0a/µ) can be varied by varying the density ρ while keeping the viscosity µ and lid velocity v0 fixed. Thus, take (in addition to the choice of the characteristic length a = 1) µ = 1 and v0 = 1 so that Re = ρ. Solve the problem for Re = 250, 500, and 750, using uniform 8 × 8 mesh of linear elements as well as 4 × 4 mesh of nine-node quadratic elements, penalty parameter γ = 108 , and convergence tolerance of = 10−3 .