High-order In-cell Discontinuous Reconstruction path-conservative methods for nonconservative hyperbolic systems -- DR.MOOD generalization
Numerical Analysis
2024-07-04 v1 Numerical Analysis
Abstract
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
Cite
@article{arxiv.2407.02931,
title = {High-order In-cell Discontinuous Reconstruction path-conservative methods for nonconservative hyperbolic systems -- DR.MOOD generalization},
author = {Ernesto Pimentel-García and Manuel J. Castro and Christophe Chalons and Carlos Parés},
journal= {arXiv preprint arXiv:2407.02931},
year = {2024}
}
Comments
Preprint. arXiv admin note: text overlap with arXiv:2105.00424