Numerical Simulation of Fuzzy Wave-Like Equations with Spatial Variable Coefficients by Lattice Boltzmann Method

In this paper, we develop a lattice Boltzmann model for a class of 1+1 dimensional nonlinear fuzzy wave-like equations with spatial variable coefficients. By choosing properly the conservation condition between the macroscopic quantity $u_{t}$ and the distribution functions and applying the Chapman-Enskog expansion, the governing equation is recovered correctly from the lattice Boltzmann equation. Moreover, the local equilibrium distribution function is obtained. The results of numerical examples have been compared with the analytical solutions to confirm good accuracy and the equilibrium of our scheme.