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arXiv · 2105.00424

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

Ernesto Pimentel-García·Manuel J. Castro·Christophe Chalons·Tomás Morales de Luna·Carlos Parés
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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.

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BibTeXRIS

Ernesto Pimentel-García, Manuel J. Castro, Christophe Chalons, Tomás Morales de Luna, Carlos Parés. 2021-05-02. In-cell Discontinuous Reconstruction path-conservative methods for non conservative hyperbolic systems -- Second-order extension. https://doi.org/10.1016/j.jcp.2022.111152

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