Comparative Study of the Accuracy of the Fundamental Mesh Structures for the Numerical Solution of Incompressible Navier-Stokes Equations in the Two-Dimensional Cavity Problem

Abstract

The accuracies of the staggered, semistaggered, vertex collocated, and cell-center collocated meshes are compared for the incompressible Navier-Stokes equations in primitive variables using the two-dimensional lid-driven cavity test problem in both the traditional form with uniform lid velocity and in the regularized form without corner discontinuities. Central differencing is used in all discretizations. The momentum equations are integrated explicitly after the solution of a Poisson pressure equation that enforces mass conservation. Richardson extrapolation is employed to estimate the correct solutions in cases without precise reference solutions. For both forms of the problem, the staggered and the cell-center collocated meshes are shown to produce comparably accurate results, while the vertex collocated mesh shows poorer accuracy. The almost unknown semistaggered mesh, which is too sensitive to the velocity discontinuity in the traditional cavity problem, appears as the most accurate mesh in the regularized cavity problem.