High-order In-cell Discontinuous Reconstruction path-conservative methods for nonconservative hyperbolic systems -- DR.MOOD generalization
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866916310492905472 |
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| author | Pimentel-García, Ernesto Castro, Manuel J. Chalons, Christophe Parés, Carlos |
| author_facet | Pimentel-García, Ernesto Castro, Manuel J. Chalons, Christophe Parés, Carlos |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02931 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | High-order In-cell Discontinuous Reconstruction path-conservative methods for nonconservative hyperbolic systems -- DR.MOOD generalization Pimentel-García, Ernesto Castro, Manuel J. Chalons, Christophe Parés, Carlos Numerical Analysis 65M08 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. |
| title | High-order In-cell Discontinuous Reconstruction path-conservative methods for nonconservative hyperbolic systems -- DR.MOOD generalization |
| topic | Numerical Analysis 65M08 |
| url | https://arxiv.org/abs/2407.02931 |