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In-cell Discontinuous Reconstruction path-conservative methods for non conservative hyperbolic systems -- Second-order extension

Authors :
Pimentel-García, Ernesto
Castro, Manuel J.
Chalons, Christophe
de Luna, Tomás Morales
Parés, Carlos
Publication Year :
2021

Abstract

We are interested in the numerical approximation of discontinuous solutions in non conservative hyperbolic systems. An extension to second-order of a new strategy based on in-cell discontinuous reconstructions to deal with this challenging topic is presented. This extension is based on the combination of the first-order in-cell reconstruction and the MUSCL-Hancock reconstruction. The first-order strategy allowed in particular to capture exactly the isolated shocks and this new second-order extension keep this property. We also set the basis of an extension to high-order methods following this in-cell methodology and a way for capturing exactly more than one shock. Several numerical tests are proposed to validate the methods for the Coupled-Burgers system, Gas dynamics equations in Lagrangian coordinates and the modified shallow water system.

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2105.00424
Document Type :
Working Paper
Full Text :
https://doi.org/10.1016/j.jcp.2022.111152