Fourier Analysis of the Effect of Grid Non-Orthogonality on the SIMPLE Algorithm

In this article, the error amplification matrix is developed for the SIMPLE algorithm formulated on the nonorthogonal grid by Fourier decomposition. The effect of grid skewness on the convergence properties of the SIMPLE algorithm is investigated in terms of robustness and convergence rate. As the grid nonorthogonality increases, the robustness of the SIMPLE algorithm, characterized by the convergence range of the pressure relaxation factor for a given velocity relaxation factor, weakens, and an effective remedy is to take the cross pressure correction terms into account rather than omit them, which is in agreement with the conclusions reached by Peric. In the case of convergence, the convergence rate seems to be strongly dependent on flow field, and the optimal rate can be reached when the grid direction coincides well with the local flow direction. The analysis also suggests that a collocated layout should be adopted in preference to a staggered layout, due to its better robustness on a nonorthogonal grid.