AIAA 98–2443 Diffusion Characteristics of Upwind Schemes on Unstructured Triangulations

The diiusive characteristics of two upwind schemes, multi-dimensional uctuation splitting and dimensionally-split nite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diiusion, and advection-diiusion. Modular coding is employed to isolate the eeects of the two approaches for upwind ux evaluation, allowing for head-to-head accuracy and ee-ciency comparisons. Both the stability of compressive limiters and the amount of artiicial diiusion generated by the schemes is found to be grid-orientation dependent, with the uctuation splitting scheme producing less artiicial diiusion than the dimensionally-split nite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2{3 seen for uctuation splitting versus nite volume when solved on the same mesh. However, accurate solutions to problems with small diiusion coeecients can be achieved on coarser meshes using uctuation splitting rather than nite volume, so that when comparing convergence rates to reach a given accuracy, uctuation splitting shows a 20{25 speedup over nite volume.