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In-cell Discontinuous Reconstruction path-conservative methods for non conservative hyperbolic systems -- Second-order extension
- 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.
- Subjects :
- Mathematics - Numerical Analysis
Mathematical Physics
Subjects
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