Edge-based reconstruction schemes for unstructured tetrahedral meshes

In this paper, we consider edge-based reconstruction (EBR) schemes for solving the Euler equations on unstructured tetrahedral meshes. These schemes are based on a high-accuracy quasi-1D reconstruction of variables on an extended stencil along the edge-based direction. For an arbitrary tetrahedral mesh, the EBR schemes provide higher accuracy in comparison with most second-order schemes at rather low computational costs. The EBR schemes are built in the framework of vertex-centered formulation for the point-wise values of variables. Here, we prove the high accuracy of EBR schemes for uniform grid-like meshes, introduce an economical implementation of quasi-one-dimensional reconstruction and the resulting new scheme of EBR family, estimate the computational costs, and give new verification results. Copyright (C) 2015 John Wiley & Sons, Ltd.