A comarative study of upwind schemes for the euler equations on unstructured grids

Abstract

Unstructured meshes offer a great deal of flexibility in the treatment of complex configurations which is difficult to match with a structured grid approach. The unstructured grid generation technique used in this study is based on Bowyer’s algorithm for the implementation of the Delaunay triangulation method. The grid generation strategy readily accommodates a smooth distribution of triangles with minimal distortion in addition to local clustering for enhanced resolution of the flow field. In the present investigation, a systematic study of upwind algorithms for Euler equations on imstructured grids has been conducted in a unified framework based on a variety of schemes. These include flux-vector splitting schemes due to Steger-Warming and Van Leer, the flux-difference splitting scheme due to Roe and the hybrid scheme AUSM (Advection Upstream Splitting Method). For simplicity, the first-order accurate versions of the schemes have been tested for a standard test case involving flow past a NACA 0012 airfoil in the subsonic, transonic and supersonic flow regimes. Comparisons with reference solutions reported in literature have been carried out.