A lattice Boltzmann method for viscous free surface waves in two dimensions


Ping Huang, Department of Environmental Science, School of Environmental Science and Engineering, Sun Yat-sen University, Guangzhou 510275, China.

E-mail: eeshping@mail.sysu.edu.cn


We propose a new method based on the combination of the lattice Boltzmann equation (LBE) and the kinematic boundary condition (KBC) method to simulate viscous free surface wave in two dimensions. In our method, the flow field is modeled by LBE, whereas the free surface is explicitly tracked by the local height function, which is calculated by the KBC method. The free surface boundary condition (FSBC) for LBE is revised from previous researches. Interpolation-supplemented lattice Boltzmann (ISLB) method is introduced, which enables our approach to be applied on arbitrary, nonuniform mesh grids. Five cases are simulated respectively to validate the LBE–KBC method: the stationary flow and the solitary waves simulated by the revised-FSBC are more accurate than the one obtained by the former-FSBC; numerical results of standing waves show that our method is compatible to the existing two-dimensional finite-volume scheme; cases of small amplitude Stokes wave and waves traveling over a submerged bar show good agreement on wave celerity, wavelength, wave amplitude and wave period between numerical results and corresponding analytical solutions and/or experiment data.Copyright © 2012 John Wiley & Sons, Ltd.