Author(s): Guglielmo Stecca; Annunziato Siviglia; Eleuterio F. Toro

Linked Author(s): Annunziato Siviglia

Keywords: No Keywords

Abstract: In this paper we develop numerical fluxes of the centred type for one-step schemes in conservative form for solving general systems of conservation laws in two space dimensions on unstructured meshes. The proposed flux is an extension of the multi-dimensional FORCE flux developed by Toro, Hidalgo and Dumbser[8]and a generalisation of the upwind biased FORCE flux (UFORCE) for structured meshes proposed by Stecca, Siviglia and Toro[6]. Here we introduce an upwind bias by modifying the shape of the staggered mesh of the original FORCE method. The upwind bias is evaluated using an estimate of the largest eigenvalue, which in any case is needed for selecting a time step. The resulting basic flux is first-order accurate and monotone. Application to non-linear systems has been done empirically via the two-dimensional inviscid shallow water equations. The proposed method improves the accuracy of the solution for small CFL numbers. It achieves comparable accuracy to that of upwind methods with approximate Riemann solvers, though retaining the simplicity and efficiency of centred methods. The performance of the scheme is assessed on test problems for the two-dimensional linear advection equation and the two-dimensional shallow water equations.

DOI:

Year: 2010