Moving-Water Equilibria Preserving HLL-Type Schemes for the Shallow Water Equations (Communications in Mathematical Research, 2020)
We construct new HLL-type moving-water equilibria preserving upwind schemes for the one-dimensional Saint-Venant system of shallow waterequations 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 schemesto accurately capture small perturbations of moving-water steady states.