Abstract This paper is devoted to the numerical analysis of the road traffic model proposed by Colombo and Goatin (J. Differ. Equ.
234(2):654–675, 2007). 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. (J. Hyperbolic Differ. Equ. 2(4):783–837,
2005) and Bürger et al. (SIAM J. Numer. Anal. 47(3):1684–1712, 2009). We reformulate accordingly the notion of entropy solution
introduced by Colombo and Goatin (J. Differ. Equ. 234(2):654–675, 2007), 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.
234(2):654–675, 2007). 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. (J. Hyperbolic Differ. Equ. 2(4):783–837,
2005) and Bürger et al. (SIAM J. Numer. Anal. 47(3):1684–1712, 2009). We reformulate accordingly the notion of entropy solution
introduced by Colombo and Goatin (J. Differ. Equ. 234(2):654–675, 2007), 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.
- Content Type Journal Article
- DOI 10.1007/s00211-009-0286-7
- Authors
- Boris Andreianov, Université de Franche-Comté Laboratoire de Mathématiques 16 route de Gray 25030 Besançon Cedex France
- Paola Goatin, ISITV, Université du Sud Toulon-Var Avenue Georges Pompidou BP 56 83162 La Valette du Var Cedex France
- Nicolas Seguin, Laboratoire J.-L. Lions, UPMC Univ Paris 06 BC 187 75252 Paris Cedex 05 France
- Journal Numerische Mathematik
- Online ISSN 0945-3245
- Print ISSN 0029-599X
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