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Article Dans Une Revue Numerische Mathematik Année : 2010

Finite volume schemes for locally constrained conservation laws

Résumé

This paper is devoted to the numerical analysis of the road traffic model proposed by Colombo and Goatin in [CG07]. The model involves a standard conservation law supplemented by a local unilateral constraint on the flux at the point x=0 (modelling a road light, a toll gate, etc.). We first show that the problem can be interpreted in terms of the theory of conservation laws with discontinuous flux function, as developed by Adimurthi et al. [AMG05] and Burger et al. [BKT09]. We reformulate accordingly the notion of entropy solution introduced in [CG07], and extend the well-posedness results to the L framework. Then, starting from a general monotone finite volume scheme for the non-constrained conservation law, we produce a simple scheme for the constrained problem and show its convergence. The proof uses a new notion of entropy process solution.Numerical examples modelling a “green wave” are presented.
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hal-00387806 , version 1 (25-05-2009)

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Paternité - Pas d'utilisation commerciale

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Boris Andreianov, Paola Goatin, Nicolas Seguin. Finite volume schemes for locally constrained conservation laws. Numerische Mathematik, 2010, 115 (4), pp. 609-645. ⟨10.1007/s00211-009-0286-7⟩. ⟨hal-00387806⟩

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