Matrix Solution Techniques for CFD Applications on Non-Uniform Grids

In this paper several different matrix solution strategies are applied to a benchmark problem discretized on a series of non-uniform grids. The problem solved is similar to the three-dimensional Poisson pressure problem, the most CPU intensive part of many CFD codes. The primary goal of this study is to determine how sensitive the various schemes are to grid aspect ratio. It is known that most methods, especially those that utilize point iteration, deteriorate when applied to non-uniform grids. It is shown that even though MG methods using point iteration as smoother break down as a stand-alone solver, they still are an effective preconditioning scheme for Krylov subspace methods. In addition, the application of these schemes to fully coupled CFD solvers as well as unstructured grids is discussed.