Effects of mesh regularity on accuracy of finite-volume schemes

The effects of mesh regularity on the accuracy of unstructured node-centered finite-volume discretizations are considered. The focus of this paper is on an edge-based approach that uses unweighted least-squares gradient reconstruction with a quadratic fit. Gradient errors and discretization errors for inviscid and viscous fluxes are separately studied according to a previously introduced methodology. The methodology considers three classes of grids: isotropic grids in a rectangular geometry, anisotropic grids typical of adapted grids, and anisotropic grids over a curved surface typical of advancing-layer viscous grids. The meshes within these classes range from regular to extremely irregular including meshes with random perturbation of nodes. The inviscid scheme is nominally third-order accurate on general triangular meshes. The viscous scheme is a nominally secondorder accurate discretization that uses an average-least-squares method. The results have been contrasted with previously studied schemes involving other gradient reconstruction methods such as the Green-Gauss method and the unweighted least-squares method with a linear fit. Recommendations are made concerning the inviscid and viscous discretization schemes that are expected to be least sensitive to mesh regularity in applications to turbulent flows for complex geometries.