Accuracy Assessment of Finite Volume Discretizations of Diffusive Fluxes on Unstructured Meshes

Abstract

The results of the 3 rd AIAA Drag Prediction Workshop showed that numerical errors are comparable in magnitude to physical modeling errors. One route to reducing numerical errors is to improve discretization accuracy on a fixed mesh. This paper presents novel techniques for analysis of truncation error for finite-volume discretizations on unstructured meshes. We apply these techniques to compare the truncation error of discretization schemes commonly used for convective flux approximation in cell-centered finite volume solvers. For that purpose, two classes of tests are considered. Analytical tests on topologically regular meshes are done to find the general form of truncation error for both linear and non-linear convection problems. Given the results of the analytic tests, a truncation error metric is defined based on the coefficients associated with the spatial derivatives in the series expansion of the truncation error. More complex numerical tests are conducted to extend the accuracy assessment to general unstructured meshes consisting of both isotropic and anisotropic triangles. We found that the choice of discretization does not change the truncation error of convective fluxes considerably on both isotropic and anisotropic meshes. Also, adding the artificial dissipation term to central discretization does not deteriorate the global accuracy of the flux integral associated with convection problems.