A well-balanced Active Flux method for the shallow water equations with wetting and drying
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BARSUKOW, Wasilij | |
| dc.contributor.author | BERBERICH, Jonas P. | |
| dc.date | 2023 | |
| dc.date.accessioned | 2024-04-04T02:36:35Z | |
| dc.date.available | 2024-04-04T02:36:35Z | |
| dc.date.issued | 2023 | |
| dc.identifier.issn | 2096-6385 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190731 | |
| dc.description.abstractEn | Active Flux is a third order accurate numerical method which evolves cell averages and point values at cell interfaces independently. It naturally uses a continuous reconstruction, but is stable when applied to hyperbolic problems. In this work, the Active Flux method is extended for the first time to a nonlinear hyperbolic system of balance laws, namely to the shallow water equations with bottom topography. We demonstrate how to achieve an Active Flux method that is well-balanced, positivity preserving, and allows for dry states in one spatial dimension. Because of the continuous reconstruction all these properties are achieved using new approaches. To maintain third order accuracy, we also propose a novel high-order approximate evolution operator for the update of the point values. A variety of test problems demonstrates the good performance of the method even in presence of shocks. | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.subject.en | finite volume methods | |
| dc.subject.en | finite volume methods | |
| dc.subject.en | Active Flux | |
| dc.subject.en | shallow water equations | |
| dc.subject.en | dry states | |
| dc.subject.en | well-balanced methods | |
| dc.title.en | A well-balanced Active Flux method for the shallow water equations with wetting and drying | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math] | |
| dc.identifier.arxiv | 2212.02426 | |
| bordeaux.journal | Communications on Applied Mathematics and Computation | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03929024 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03929024v1 | |
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