High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems

High‐order in‐cell discontinuous reconstruction path‐conservative methods for nonconservative hyperbolic systems–DR.MOOD method

Published:2024-08 Issue: Volume: Page:
ISSN:0749-159X
Container-title:Numerical Methods for Partial Differential Equations
language:en
Short-container-title:Numerical Methods Partial

Author:

Pimentel‐García Ernesto¹^ORCID,Castro Manuel J.¹,Chalons Christophe²,Parés Carlos¹

Affiliation:

1. Departamento de Análisis Matemático, Estadística e Investigación Operativa, y Matemática aplicada Universidad de Málaga Málaga Spain

2. Laboratoire de Mathématiques de Versailles UVSQ, CNRS, Université Paris‐Saclay Versailles France

Abstract

AbstractIn 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.

Funder

European Commission

Publisher

Wiley

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/num.23133

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