Displaying similar documents to “Godunov method for nonconservative hyperbolic systems”

On the well-balance property of Roe’s method for nonconservative hyperbolic systems. Applications to shallow-water systems

Carlos Parés, Manuel Castro (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to introduce a general concept of well-balancing for numerical schemes solving this kind of systems. Once this concept stated, we investigate the well-balance properties of numerical schemes based on the generalized Roe linearizations introduced by [Toumi, J. Comp. Phys. 102 (1992) 360–373]. Next, this general theory is applied to obtain...

Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint

Florent Berthelin (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.

The numerical interface coupling of nonlinear hyperbolic systems of conservation laws : II. The case of systems

Edwige Godlewski, Kim-Claire Le Thanh, Pierre-Arnaud Raviart (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We study the theoretical and numerical coupling of two hyperbolic systems of conservation laws at a fixed interface. As already proven in the scalar case, the coupling preserves in a weak sense the continuity of the solution at the interface without imposing the overall conservativity of the coupled model. We develop a detailed analysis of the coupling in the linear case. In the nonlinear case, we either use a linearized approach or a coupling method based on the solution of a Riemann...