Commun. Comput. Phys., 12 (2012), pp. 1183-1214.


A Finite Volume Upwind-Biased Centred Scheme for Hyperbolic Systems of Conservation Laws: Application to Shallow Water Equations

Guglielmo Stecca 1*, Annunziato Siviglia 1, Eleuterio F. Toro 2

1 Department of Civil and Environmental Engineering, University of Trento, Via Mesiano 77, I-38100 Trento, Italy.
2 Laboratory of Applied Mathematics, University of Trento, Via Mesiano 77, I-38100 Trento, Italy.

Received 18 May 2011; Accepted (in revised version) 7 December 2011
Available online 17 April 2012
doi:10.4208/cicp.180511.071211a

Abstract

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 of the UFORCE method developed by Stecca, Siviglia and Toro [25], in which the upwind bias for the modification of the staggered mesh is evaluated taking into account the smallest and largest wave of the entire Riemann fan. The proposed first-order method is shown to be identical to the Godunov upwind method in applications to a 2x2 linear hyperbolic 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 in the finite volume framework on unstructured meshes. Finally, numerical comparison with current competing numerical methods enables us to identify the salient features of the proposed method.

AMS subject classifications: 65M08, 76M12

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Key words: Conservative hyperbolic systems, centred schemes, unstructured meshes, numerical fluxes, shallow water equations, FORCE, upwind-biased.

*Corresponding author.
Email: guglielmo.stecca@ing.unitn.it (G. Stecca), nunzio.siviglia@ing.unitn.it (A. Siviglia), toroe@ing.unitn.it (E. F. Toro)
 

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