An efficient finite difference method for the shallow water equations

A high-order explicit finite difference scheme is derived solving the shallow water equations. The boundary closures are based on the diagonal-norm summation-by-parts (SBP) framework and the boundary conditions are imposed using a penalty (SAT) technique. Flux-splitting combined with upwind SBP operators is used to naturally introduce artificial dissipation. The scheme is tested against various benchmark problems where high-order convergence is verified for smooth solutions. A particular discretization of the source term is used leading to a well-balanced scheme. We also present an application: A simplified incident wave simulation with wave-channel interaction using a multi-block setup. Experiments suggest that a bathymetry consisting of many spikes could provide a dispersing effect on an incoming wave. (C) 2020 Elsevier Inc. All rights reserved.