RT Journal Article
T1 In-cell discontinuous reconstruction path-conservative methods for non conservative hyperbolic systems - Second-order extension
A1 Pimentel García, Ernesto
A1 Castro-Díaz, Manuel Jesús
A1 Chalons, Christophe
A1 Morales-de-Luna, Tomás
A1 Parés-Madroñal, Carlos María
K1 Método de los volúmenes finitos
AB 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 with the standard 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. Moreover, the well-balanced property of the method is also studied. 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.
PB Elsevier
YR 2022
FD 2022-06-15
LK https://hdl.handle.net/10630/24330
UL https://hdl.handle.net/10630/24330
LA eng
NO Pimentel García, Ernesto,  Castro, Manuel J.,  Chalons, Christophe,  Morales de Luna, Tomás,  Pares-Madroñal, Carlos Maria, "In-cell discontinuous reconstruction path-conservative methods for non conservative hyperbolic systems - Second-order extension. In-cell discontinuous reconstruction path-conservative methods for non conservative hyperbolic systems - Second-order extension". Journal of Computational Physics Volume 459, 15 June 2022, 111152.  https://doi.org/10.1016/j.jcp.2022.111152
NO The research of CP, MC and EPG was partially supported by the Spanish Government (SG), the European Regional Development Fund (ERDF), the Regional Government of Andalusia (RGA), and the University of Málaga (UMA) through the projects of reference RTI2018-096064-B-C21 (SG-ERDF), UMA18-Federja-161 (RGA-ERDF-UMA), and P18-RT-3163 (RGA-ERDF). EPG was also financed by the Junior Scientific Visibility Program from the Foundation Mathématiques Jacques Hadamard for a stay of three month in the Laboratoire de Mathématiques de Versailles (LMV) with reference ANR-11-LABX-0056-LMH, LabEx LMH. TML was supported by the Spanish Government (SG) through the projects of reference RTI2018-096064-B-C22. The authors thank the anonymous reviewer whose comments helped to improve the paper. Funding for open access charge: Universidad de Málaga / CBUA
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 20 ene 2026