English

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

R2 v1 2026-06-28T17:27:39.065Z