Vertex-centroid finite volume scheme on tetrahedral grids for conservation laws

TL;DR

This paper introduces improved vertex-centroid finite volume schemes on tetrahedral grids for conservation laws, featuring a new interpolation method, a simplified reconstruction, and stability enhancements for scalar laws, applied to Euler equations.

Contribution

It proposes a novel interpolation scheme with positive weights and a simplified, more accurate reconstruction method for vertex-centroid schemes on tetrahedral grids.

Findings

Enhanced interpolation scheme with positive weights

More accurate and efficient reconstruction scheme

Stable limited schemes for scalar conservation laws

Abstract

Vertex-centroid schemes are cell-centered finite volume schemes for conservation laws which make use of vertex values to construct high resolution schemes. The vertex values must be obtained through a consistent averaging (interpolation) procedure. A modified interpolation scheme is proposed which is better than existing schemes in giving positive weights in the interpolation formula. A simplified reconstruction scheme is also proposed which is also more accurate and efficient. For scalar conservation laws, we develop limited versions of the schemes which are stable in maximum norm by constructing suitable limiters. The schemes are applied to compressible flows governed by the Euler equations of inviscid gas dynamics.