In-cell discontinuous reconstruction path-conservative methods for non conservative hyperbolic systems - Second-order extension

Ernesto Pimentel-García (1) , Manuel Jesús Castro (1) , Christophe Chalons (2) , Tomás Morales de Luna (3) , Carlos Parés (1)

1 Universidad de Málaga [Málaga] = University of Málaga [Málaga]
2 LMV - Laboratoire de Mathématiques de Versailles
3 Universidad de Córdoba = University of Córdoba [Córdoba]

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.

Mots clés: Finite volume methods; In-cell reconstruction; MUSCL-Hancock; Nonconservative hyperbolic systems; Path-conservative methods; Shock-capturing methods

Domaines: Analyse numérique [math.NA]

Ernesto Pimentel-García, Manuel Jesús Castro, Christophe Chalons, Tomás Morales de Luna, Carlos Parés. In-cell discontinuous reconstruction path-conservative methods for non conservative hyperbolic systems - Second-order extension. Journal of Computational Physics, 2022, 459, pp.111152. ⟨10.1016/j.jcp.2022.111152⟩. ⟨hal-03703593⟩