Klingenberg, Christian; Kurganov, Alexander; Liu, Yongle; Zenk, Markus Moving-water equilibria preserving HLL-type schemes for the shallow water equations. (English) Zbl 1463.76035 Commun. Math. Res. 36, No. 3, 247-271 (2020). Summary: We construct new Harten-Lax-van Leer (HLL)-type moving-water equilibria preserving upwind schemes for the one-dimensional Saint-Venant system of shallow water equations with nonflat bottom topography. The designed first- and second-order schemes are tested on a number of numerical examples, in which we verify the well-balanced property as well as the ability of the proposed schemes to accurately capture small perturbations of moving-water steady states. Cited in 7 Documents MSC: 76M12 Finite volume methods applied to problems in fluid mechanics 65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs 86A05 Hydrology, hydrography, oceanography Keywords:shallow water equations; Harten-Lax-van Leer scheme; well-balanced method; steady-state solutions; moving-water and still-water equilibria PDFBibTeX XMLCite \textit{C. Klingenberg} et al., Commun. Math. Res. 36, No. 3, 247--271 (2020; Zbl 1463.76035) Full Text: DOI