Performance Comparison of Multidimensional Residual Distribution Methods to Godunov-Type Finite-Volume Methods

摘要

While it is apparent that residual-distribution methods can obtain higher accuracy than finite-volume methods on similar meshes, there have not been many studies that compared the performance of the two approaches in a systematic and quantitative manner. In this study, solutions are obtained for problems of circular advection, subsonic inviscid flow past a cylinder, and Ringleb's flow. For each case, the accuracy of the spatial discretization is assessed by examining the L_2-error norm of a given quantity and its dependence on the mesh size. The examples seem to indicate that linear second-order residual-distribution schemes are about half an order of magnitude more accurate than finite-volume methods. Unfortunately, non-linear residual-distribution schemes that are both second-order and monotone appear to suffer a penalty in accuracy to the extent that they can be even worse than finite-volume methods. The conclusions acknowledge the potential of residual-distribution methods to be more accurate but express dissatisfaction with current non-linear distribution schemes.