Preserving stationary discontinuities in two-layer shallow water equations with a novel well-balanced approach
| Autor: | Majid Akbari, Bahareh Pirzadeh |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Journal of Hydroinformatics, Vol 25, Iss 5, Pp 1979-2003 (2023) |
| Druh dokumentu: | article |
| ISSN: | 1464-7141 1465-1734 |
| DOI: | 10.2166/hydro.2023.312 |
| Popis: | This paper proposes a novel energy-balanced numerical scheme for the two-layer shallow water equations (2LSWEs) that accurately captures internal hydraulic jumps without introducing spurious oscillations. The proposed scheme overcomes the problem of post-shock oscillations in the 2LSWE, a phenomenon commonly observed in numerical solutions of non-linear hyperbolic systems when shock-capturing schemes are used. The approach involves reconstructing the internal momentum equation of 2LSWEs using the correct Hugoniot curve via a set of shock wave fixes originally developed for single-layer shallow water equations. The scheme successfully preserves all stationary solutions, making it highly suitable for simulations of real-life scenarios involving small perturbations of these conditions. HIGHLIGHTS The paper proposes a remedy to the problem of post-shock oscillations in the two-layer shallow water equations.; It is an extension of a family of well-balanced and shock-resolving schemes that were originally developed for single-layer shallow water equations.; The resulting scheme, called HLL-MSF, successfully preserves all stationary solutions, including those with shock discontinuities.; |
| Databáze: | Directory of Open Access Journals |
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