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Pimentel García, Ernesto Castro-Díaz, Manuel Jesús Chalons, Christophe Morales-de-Luna, Tomás Parés-Madroñal, Carlos María 2022-06-09T11:41:59Z 2022-06-09T11:41:59Z 2022-06-15 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 https://hdl.handle.net/10630/24330 10.1016/j.jcp.2022.111152 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. eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Método de los volúmenes finitos In-cell discontinuous reconstruction path-conservative methods for non conservative hyperbolic systems - Second-order extension journal article