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 - <p style="text-align: justify;">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.</p>