High-order in-cell discontinuous reconstruction path-conservative methods for nonconservative hyperbolic systems–DR.MOOD method - Pimentel García, Ernesto; Castro-Díaz, Manuel Jesús; Chalons, Christophe; Parés-Madroñal, Carlos María (Wiley, 2024)
In this work, we develop a new framework to deal numerically with discontinuous solutions in nonconservative hyperbolic systems. First an extension of the MOOD methodology to nonconservative systems based on Taylor expansions is presented. This extension combined with an in-cell discontinuous reconstruction operator are the key points to develop a new family of high-order methods that are able to capture exactly isolated shocks. Several test cases are proposed to validate these methods for the Modified Shallow Water equations and the Two-Layer Shallow Water system.
Keywords: Ecuaciones en derivadas parciales; Ecuaciones diferenciales hiperbólicas; Análisis numérico; Análisis matemático; Matemáticas aplicadas; Finite volume methods; In-cell discontinuous reconstructions; MOOD; Nonconservative hyperbolic systems; Path-conservative methods; Shock-capturing methods; Two-layer shallow water equations