Well-Balanced High-Order MUSTA Schemes for Non-Conservative Hyperbolic Systems

M. J. Castro (), C. Parés, A. Pardo and E. F. Toro
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M. J. Castro: U. de Málaga, Depto. de Análisis mátematico
C. Parés: U. de Málaga, Depto. de Análisis mátematico
A. Pardo: U. de Málaga, Depto. de Análisis mátematico
E. F. Toro: University of Trento, Laboratory of Applied Mathematics. Faculty of Engineering

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 249-256 from Springer

Abstract: Abstract We introduce a Multi-Stage (MUSTA) approach for constructing upwind numerical schemes for nonconservative hyperbolic systems. MUSTA schemes for hyperbolic conservation laws were introduced in [8] as an approximate Riemann solver based on a GFORCE scheme and a predictor-corrector procedure. In [2] a path-conservative GFORCE numerical scheme (in the sense introduced in [6]) for nonconservative hyperbolic systems is proposed. Here, we propose a predictor-corrector procedure based on this extension of GFORCE to obtain a generalization of MUSTA schemes. These schemes can be applied to systems of conservation laws with source terms and nonconservative products. In particular, some applications to two-layer shallow-water flows are presented.

Keywords: Numerical Scheme; Riemann Problem; Reconstruction Operator; Nonconservative System; Approximate Riemann Solver (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/978-3-540-69777-0_29

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