Free surface water wave 1-D LBGK predictions

Abstract

The performance of a single phase free surface lattice Boltzmann (LB) solver is investigated. The lattice-BGK (LBGK) model explores the free surface behavior with a focus on non-overturning water waves. The discretized equations are based on shallow water wave theory in viscous flow. Therefore, only flows with horizontal velocity dominating free surface waves is applicable. The solutions on uniform grids implement an elastic-collision scheme assuming slip boundaries at the tank walls. Simulations are carried out in horizontal base-excited square tanks. The forcing amplitude and the tank aspect ratios of are kept constant while the forcing frequency is varied off- and near resonance. At this water depth, the free surface was observed to slosh in a first sway mode initially; however, the following cycles would typically consist of traveling waves or bores. The flow typically remained 1-D in resonance cases except at the bore front and near the walls. The LB experiments are limited to flow simulations of weak bores which occurred near resonance with forcing amplitude in the order of . The LB solutions were in good agreement with a Riemann solver and agreed fairly well with experimental data.