Central unstaggered finite volume schemes for hyperbolic systems: Applications to unsteady shallow water equations

Abstract

A class of central unstaggered finite volume methods for approximating solutions of hyperbolic systems of conservation laws is developed in this paper. The proposed method is an extension of the central, non-oscillatory, finite volume method of Nessyahu and Tadmor (NT). In contrast with the original NT scheme, the method we develop evolves the numerical solution on a single grid; however ghost cells are implicitly used to avoid the resolution of the Riemann problems arising at the cell interfaces. We apply our method and solve classical one and two-dimensional unsteady shallow water problems. Our numerical results compare very well with those obtained using the original NT method, and are in good agreement with corresponding results appearing in the recent literature, thus confirming the efficiency and the potential of the proposed method.