A Finite Volume Upwind-Biased Centred Scheme for Hyperbolic Systems of Conservation Laws: Application to Shallow Water Equations (Communications in Computational Physics, 2012)
We construct a new first-order central-upwind numerical method for solving systems of hyperbolic equations in conservative form. It applies in multidimensional structured and unstructured meshes. The proposed method is an extension ofthe UFORCE method developed by Stecca, Siviglia and Toro [25], in which the upwindbias for the modification of the staggered mesh is evaluated taking into account thesmallest and largest wave of the entire Riemann fan. The proposed first-order methodis shown to be identical to the Godunov upwind method in applications to a 2×2 linearhyperbolic system. The method is then extended to non-linear systems and its performance is assessed by solving the two-dimensional inviscid shallow water equations.Extension to second-order accuracy is carried out using an ADER-WENO approach inthe finite volume framework on unstructured meshes. Finally, numerical comparisonwith current competing numerical methods enables us to identify the salient featuresof the proposed method.