Communications in Mathematical Sciences

Volume 18 (2020)

Number 1

Path-conservative in-cell discontinuous reconstruction schemes for non conservative hyperbolic systems

Pages: 1 – 30



Christophe Chalons (Laboratoire de Mathématiques de Versailles, Université de Versailles Saint-Quentin, Université Paris-Saclay, Versailles, France)


We are interested in the numerical approximation of discontinuous solutions in nonconservative hyperbolic systems. We introduce the basics of a new strategy based on in-cell discontinuous reconstructions to deal with this challenging topic, and apply it to a 2x2 non-conservative toy model, and a 3x3 gas dynamics system in Lagrangian coordinates. The strategy allows in particular to compute exactly isolated shocks. Numerical evidences are proposed.


non-conservative hyperbolic systems, path conservative schemes, in-cell discontinuous reconstructions, discontinuous solutions, shock waves.

2010 Mathematics Subject Classification

35L40, 65M99, 76M12, 76N15

Received 24 November 2018

Accepted 2 August 2019

Published 1 April 2020