| Abstract: | Nine finite difference schemes using primitive variables on various grid arrangements were systematically tested on a benchmark problem of two-dimensional incompressible Navier–Stokes flows. The chosen problem is similar to the classical lid-driven cavity flow, but has a known exact solution. Also, it offers the reader an opportunity to thoroughly evaluate accuracies of various conceptual grid arrangements. Compared to the exact solution, the non-staggered grid scheme with higher-order accuracy was found to yield an accuracy significantly better than others. In terms of ‘overall performance’, the so-called 4/1 staggered grid scheme proved to be the best. The simplicity of this scheme is the primary benefit. Furthermore, the scheme can be changed into a non-staggered grid if the pressure is replaced by the pressure gradient as a field variable. Finally, the conventional staggered grid scheme developed by Harlow and Welch also yields relatively high accuracy and demonstrates satisfactory overall performance. |
