Effects of mesh regularity on accuracy of finite-volume sche mes

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 dis cretization 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. Re commendations 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.

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