Transport-equilibrium schemes for computing nonclassical shocks

This Note presents a very efficient numerical strategy for computing weak solutions of a scalar conservation law which fails to be genuinely nonlinear. In such a situation, the dynamics of shock solutions turns out to be mainly driven by a prescribed kinetic function that imposes the speed of propagation of the discontinuities. We show how to enforce the validity of the kinetic criterion at the discrete level. The resulting scheme provides, in addition, sharp profiles. Numerical evidence are included. To cite this article: C. Chalons, C. R. Acad. Sci. Paris, Ser. I 342 (2006).