Title: A simple LBE wave runup model

Authors: J.B. Frandsen

Addresses: School of Civil Engineering, University of Sydney, NSW 2006, Australia

Abstract: The suitability of a Lattice Bhatnagar-Gross-Krook (LBGK) modelling approach is tested to examine the behaviour of free surface waves in shallow water. The free surface model is fully non-linear. Mathematically, this is taken into account through the collision integral. The present LBGK model discretises the non-linear shallow water equation in rotational flow and approximates the collision between particles using a single time relaxation. It is further assumed that the waves do not overturn. The test case includes a long-wave run-up study on a sloping beach. Two methods have been evaluated to treat the wet-dry interface: a thin film in dry areas of the beach slope; a linear extrapolation scheme. The standard LBGK solutions are second-order accurate in space and first-order accurate in time. The uniform grid solutions compared well with other findings reported in the literature when using a shoreline algorithm.

Keywords: wave run-up; lattice Boltzmann method; LBM; BGK approximation; Bhatnagar-Gross-Krook; tsunami; modelling; free surface waves; shallow water; rotational flow; sloping beaches; wet-dry interface.

DOI: 10.1504/PCFD.2008.018093

Progress in Computational Fluid Dynamics, An International Journal, 2008 Vol.8 No.1/2/3/4, pp.222 - 232

Published online: 30 Apr 2008 *

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