Finite Volume Diffusion Operators for Compressible CFD on Unstructured Grids

Abstract

A survey of diffusion operators for compressible CFD solvers on unstructured grids is conducted to understand different formulation procedures for viscous fluxes. A patch-wise version of the method of manufactured solutions is used to test the robustness and accuracy of the diffusion operators. These diffusion operators are tested and compared on different mesh topologies in 1D and 2D to study the effect of mesh quality, mesh resolution, and the solution behavior. In 1D the mesh quality is determined by stretching the mesh by a constant factor, whereas in 2D the mesh quality includes stretching, aspect ratio, skewness, and curvature. Insight into the role of mesh quality on the diffusion terms is gained by examining the truncation error for diffusion terms evaluated with central differences in transformed coordinates. Quantities examined include the numerical approximation errors and order of accuracy associated with face gradient reconstruction and diffusion term integration. In addition, the positivity of the diffusion term is examined which provides a measure of the numerical stability of the gradient operators. In the present work, the testing of diffusion operators is limited to cell-centered finite volume methods that are formally second order accurate.