On Path-Conservative Numerical Schemes for Hyperbolic Systems of Balance Laws

M. L. Muñoz-Ruiz () and C. Parés ()
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M. L. Muñoz-Ruiz: Universidad de Málaga, Dept. Matemática Aplicada
C. Parés: Universidad de Málaga, Dept. Análisis Matemático

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 305-312 from Springer

Abstract: Abstract This work is concerned with the numerical approximation of Cauchy problems for one-dimensional hyperbolic systems of conservation laws with source terms or balance laws. These systems can be studied as a particular case of nonconservative hyperbolic systems [3, 4, 5]. The theory developed by Dal Maso, LeFloch and Murat [2] is used to define a concept of weak solutions of nonconservative systems based on the choice of a family of paths in the phase space. The notion of path-conservative numerical scheme introduced in [6], which generalizes that of conservative scheme for conservative systems, is also related to the choice of a family of paths. In this work we present an appropriate choice of paths in order to define the concept of weak solution (see [1, 8]) in the particular case of balance laws, together with the notion of path-conservative numerical scheme for this particular case and some properties. We also consider the well-balance property of these schemes and the consistency with the definition of weak solutions, with a result pointing in the direction of a Lax-Wendroff type convergence result.

Keywords: Weak Solution; Hyperbolic System; Riemann Problem; Integral Curve; Nonconservative System (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69777-0_36

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DOI: 10.1007/978-3-540-69777-0_36

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