## A Well-Balanced Scheme Using Non-Conservative Products Designed for Hyperbolic Systems of Conservation Laws With Source Terms (2001)

Citations: | 21 - 3 self |

### BibTeX

@MISC{Gosse01awell-balanced,

author = {Laurent Gosse},

title = {A Well-Balanced Scheme Using Non-Conservative Products Designed for Hyperbolic Systems of Conservation Laws With Source Terms},

year = {2001}

}

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### Abstract

The aim of this paper is to present a new kind of numerical processing for hyperbolic systems of conservation laws with source terms. This is achieved by means of a non-conservative reformulation of the zero-order terms of the right-hand-side of the equations. In this context, we decided to use the results of DalMaso, LeFloch and Murat [9] about non-conservative products, and the generalized Roe matrixes introduced by Toumi [36] to derive a first-order linearized well-balanced scheme in the sense of Greenberg and LeRoux [19]. As a main feature, this approach is able to preserve the right asymptotic behaviour of the original inhomogeneous system [31], which is not a obvious property [6]. Numerical results for the Euler equations are shown to handle correctly these equilibria in various situations. Key words: conservation laws, source terms. nonconservative products, balanced scheme. AMS subjects classification: 65M06, 76N15. 1 Current adress: Foundation for Research and Technology Hel...