The purpose of this work is to make a review of recent results developed by the author and collaborators, on the development of efficient incomplete multidimensional Riemann solvers for hyperbolic systems. We present a general strategy for constructing genuinely two-dimensional Riemann solvers, that can be applied for solving systems including source and coupling terms. Two-dimensional effects are taken into account through the approximate solutions of 2d Riemann problems arising at the vertices of the computational mesh. Applications to shallow water systems are presented.

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Multidimensional Approximate Riemann Solvers for Hyperbolic Nonconservative Systems: A Review

  • José M. Gallardo

摘要

The purpose of this work is to make a review of recent results developed by the author and collaborators, on the development of efficient incomplete multidimensional Riemann solvers for hyperbolic systems. We present a general strategy for constructing genuinely two-dimensional Riemann solvers, that can be applied for solving systems including source and coupling terms. Two-dimensional effects are taken into account through the approximate solutions of 2d Riemann problems arising at the vertices of the computational mesh. Applications to shallow water systems are presented.