Communications in Mathematical Sciences
Volume 18 (2020)
Path-conservative in-cell discontinuous reconstruction schemes for non conservative hyperbolic systems
Pages: 1 – 30
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