The Riemann problem for two-layer shallow water equations with bottom topography

Autor:	Wang Fan, Sheng Wancheng, Hu Yanbo, Zhang Qinglong
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	the riemann problem laminar shallow water equations riemann invariants the stationary wave rankine-hugoniot condition primary: 35l40 76l05 76m12 35l65 secondary: 35f55 Analysis QA299.6-433
Zdroj:	Advances in Nonlinear Analysis, Vol 13, Iss 1, Pp 1603-1627 (2024)
Druh dokumentu:	article
ISSN:	2191-950X 2024-0058
DOI:	10.1515/anona-2024-0058
Popis:	In this article, we propose a model describing laminar shallow water flows with two velocities to handle an uneven bottom. The model is established by taking the different velocities into account. The source terms generated from the bottom topography prevent us from solving the Riemann problem directly. We first derive the elementary waves including the stationary wave where the global entropy condition is used to ensure uniqueness. Then, we analyze the resonance phenomenon and coalescence of waves by classifying the initial data into different regions. Finally, the Riemann problem is resolved explicitly on a case-by-case basis.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/1e26dc13639e4423b0987e4620ea0649 Zobrazit plný text záznamu View record in DOAJ