LATTICE BOLTZMANN SIMULATIONS OF DISCONTINUOUS FLOWS

Abstract

The lattice Boltzmann model for the shallow water equations (LABSWE) is applied to the simulation of certain discontinuous flows. Curved boundaries are treated efficiently, using either the elastic-collision scheme for slip and semi-slip boundary conditions or the bounce-back scheme for no-slip conditions. The force term is accurately determined by means of the centred scheme. Simulations are presented of a small pulse-like perturbation of the still water surface, a dam break, and a surge wave interaction with a circular cylinder. The results agree well with predictions from alternative high-resolution Riemann solver based methods, demonstrating the capability of LABSWE to predict shallow water flows containing discontinuities.