High-order In-cell Discontinuous Reconstruction path-conservative methods for nonconservative hyperbolic systems -- DRMOOD generalization
<|reference_start|>High-order In-cell Discontinuous Reconstruction path-conservative methods for nonconservative hyperbolic systems -- DRMOOD generalization: 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.<|reference_end|>
@article{pimentel-garcía2024high-order,
    title={High-order In-cell Discontinuous Reconstruction path-conservative
  methods for nonconservative hyperbolic systems -- DR.MOOD generalization},
    author={Ernesto Pimentel-Garc'ia, Manuel J. Castro, Christophe Chalons,
  Carlos Par'es},
    journal={arXiv preprint arXiv:2407.02931},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.02931},
    primaryClass={math.NA cs.NA}
}