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

In this paper, the Cartesian velocity components and the covariant velocity components are adopted respectively as the main variables in solving the m omentum equations in the SIMPLE-like method to calculate a lid-driven cavit y flow on non-orthogonal collocated grids. In total, more than 400 computer runs are carried out for a two-dimensional problem. The accuracy and conve rgence 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 vel ocity method if the relaxation factor for pressure is small enough. However , the convergence range of the relaxation factor for pressure in the covari ant velocity method is quite narrow. When the cross-derivatives in the pres sure-correction equation are retained approximately, its convergence perfor mance can be greatly improved. Copyright (C) 1999 John Wiley & Sons, Ltd.