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High order extensions of roe schemes for two-dimensional nonconservative hyperbolic systems. (English) Zbl 1203.65131
Summary: This paper is concerned with the development of well-balanced high order Roe methods for two-dimensional nonconservative hyperbolic systems. In particular, we are interested in extending the methods introduced by M. J. Castro et al. [Math. Comput. 75, No. 255, 1103–1134 (2006; Zbl 1096.65082)] to the two-dimensional case. We also investigate the well-balance properties and the consistency of the resulting schemes. We focus in applications to one and two layer shallow water systems.

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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