Comparison of using Cartesian and covariant velocity components on non‐orthogonal collocated grids

Abstract

In this paper, the Cartesian velocity components and the covariant velocity components are adopted respectively as the main variables in solving the momentum equations in the SIMPLE-like method to calculate a lid-driven cavity flow on non-orthogonal collocated grids. In total, more than 400 computer runs are carried out for a two-dimensional problem. The accuracy and convergence performance of using Cartesian and covariant velocity components are compared in detail. Comparisons show that both the Cartesian and covariant velocity methods have the same numerical accuracy. The convergence rate of the covariant velocity method can be faster than that of the Cartesian velocity method if the relaxation factor for pressure is small enough. However, the convergence range of the relaxation factor for pressure in the covariant velocity method is quite narrow. When the cross-derivatives in the pressure-correction equation are retained approximately, its convergence performance can be greatly improved. Copyright © 1999 John Wiley & Sons, Ltd.