Mesh Quality Effects on the Accuracy of Euler and Navier-Stokes Solutions on Unstructured Meshes

We examine discretization error for standard node- and cell-centered schemes using the Method of Manufactured Solutions. We find that for isotropic grids, node-centered approaches produce less error than cell-centered approaches for comparable cell size. In contrast, cell-centered schemes produce less discretization error on stretched meshes. In 3D, careful treatment of non-planar faces is necessary to avoid first-order errors. We introduce a new corrected scheme which enhances the accuracy of the node-centered scheme to third-order.