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Vertex-centroid schemes are cell-centered finite volume schemes forconservation laws which make use of vertex values to construct high resolutionschemes. The vertex values must be obtained through a consistent averaging(interpolation) procedure. A modified interpolation scheme is proposed which isbetter than existing schemes in giving positive weights in the interpolationformula. A simplified reconstruction scheme is also proposed which is also moreaccurate and efficient. For scalar conservation laws, we develop limitedversions of the schemes which are stable in maximum norm by constructingsuitable limiters. The schemes are applied to compressible flows governed bythe Euler equations of inviscid gas dynamics.

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