Comparison of solution accuracy of multidimensional residual distribution and Godunov-type finite-volume methods

While it is apparent that residual distribution (RD) methods generally offer higher accuracy than finite volume (FV) methods on similar meshes, few studies have directly compared the performance of the two approaches in a systematic and quantitative manner. In this study, solutions are obtained for scalar equations and the Euler equations governing two-dimensional inviscid compressible gaseous flows. Comparisons between RD and FV are made for smooth and discontinuous flows solved on structured quadrilateral meshes. Since the RD method is applied on simplexes, the effect of tessellating the quadrilaterals into triangles by aligning the diagonal with the characteristic vectors is explored. The accuracy of the spatial discretisation is assessed by examining the L 1-error norm of a given quantity and its dependence on the grid size. For the Euler equations, two methods of distributing the system are used: system decomposition and matrix distribution. The results indicate that RD schemes can indeed surpass FV schemes in terms of solution accuracy. However, it is also shown that standard non-linear RD schemes can suffer from a degradation in accuracy to the extent that they can become even less accurate than FV methods. Furthermore, numerical difficulties were encountered in some solutions obtained with the RD schemes, particularly for the case of steady subsonic flow around a circular cylinder.

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