TY - JOUR T1 - Moving-Water Equilibria Preserving HLL-Type Schemes for the Shallow Water Equations AU - Klingenberg , Christian AU - Kurganov , Alexander AU - Liu , Yongle AU - Zenk , Markus JO - Communications in Mathematical Research VL - 3 SP - 247 EP - 271 PY - 2020 DA - 2020/07 SN - 36 DO - http://doi.org/10.4208/cmr.2020-0013 UR - https://global-sci.org/intro/article_detail/cmr/17848.html KW - Shallow water equations, Harten-Lax-Van Leer (HLL) scheme, well-balanced method, steady-state solutions (equilibria), moving-water and still-water equilibria. AB -

We construct new 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.