  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.
