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.

The performance of the unified finite approaches exponential-type scheme (UNIFAES) for advective and diffusive transport equations, for the incompressible Navier-Stokes equations in primitive variables, is evaluated by comparison with the central differencing and the exponential scheme. Staggered, semistaggered, vertex collocated, and cell-center collocated meshes are considered. The Cartesian two-dimensional lid-driven cavity test problem is employed both in its traditional form with uniform lid velocity and in the regularized form without corner discontinuities. Richardson extrapolation is employed to produce reference results in the cases without prior precise reference solutions. The UNIFAES shows accuracy generally superior to the other schemes and stability even at the highest Reynolds numbers employed. This article also completes a previous comparative study of the performance of the mesh structures, generalizing the results there observed for higher Reynolds numbers and for schemes other than central differencing.

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