Direct simulations of the linear elastic displacements field based on a lattice Boltzmann model

In this paper, a lattice Boltzmann model for simulating linear elastic Lame equation is proposed. Differently from the classic lattice Boltzmann models, this lattice Boltzmann model is based on displacement distribution function in lattice Boltzmann equation. By using the technique of the higher-order moments of equilibrium distribution functions and a series of partial differential equations in different time scales, we obtain the Lame equation with fourth-order truncation errors. Based on this model, some problems with small deflection are simulated. The comparisons between the numerical results and the analytical solutions are given in detail. The numerical examples show that the lattice Boltzmann model can be used to solve problems of the linear elastic displacement field with small deflection. Copyright (c) 2015 John Wiley & Sons, Ltd.