On Robust and Accurate Arbitrary Polytope CFD Solvers

Abstract

In recent years there has been signican t interest in nite-v olume schemes applied to meshes composed of arbitrary polytopes. These generalized meshes are an extension of more traditional meshes composed either entirely of simplex elements, or the four traditional element topologies (hexahedra, pyramid, prism, and tetrahedra). These mesh types can simplify mesh generation and adaptation, in particular by admitting so called \hanging nodes in the mesh topology. However, many of the algorithms typically employed for unstructured grids either reduce to rst order accuracy or exhibit unstable behavior on these generalized meshes. In this paper, we discuss several examples of these behaviors. Finally we describe our solution to some of the given shortcomings as well as document current outstanding issues.