Nature of Driven Cavity Flow at High-Re and Benchmark Solutions on Fine Grid Mesh

The numerical solutions of 2-D steady incompressible flow in a driven cavity are presented. The Navier-Stokes equations in streamfunction and vorticity variables are solved simply with Successive Over Relaxation (SOR) method. Using a very fine grid mesh with 1025 × 1025 points, the steady driven cavity flow is solved for Re ≤ 20,000. For accuracy, the iterations are carried out on the streamfunction and vorticity variables until the steady streamfunction and vorticity equations are satisfied with a residual that were less than 10−10. Interesting features of the flow are presented in detail. The nature of the driven cavity flow at high Reynolds numbers is discussed in detail in terms of physical and mathematical and also numerical aspects, in an attempt to address the controversy on this flow problem at high Reynolds numbers.