The lid-driven square cavity flow: Numerical solution with a 1024 x 1024 grid

Abstract

The problem of flow inside a square cavity whose lid has constant velocity is solved. This problem is modeled by the Navier-Stokes equations. The numerical model is based on the finite volume method with numerical approximations of second-order accuracy and multiple Richardson extrapolations (MRE). The iterative process was repeated until the machine round-off error achievement. This work presents results for 42 variables of interest, and their discretization errors estimates, on the 1024 x 1024 nodes grid and the following Reynolds numbers: 0.01, 10, 100, 400 and 1000. These results are compared with sixteen sources in literature. The numerical solutions of this work are the most accurate obtained for this problem to date. The use of multiple Richardson extrapolations reduces the discretization error significantly. Copyright © 2009 by ABCM.