A lattice Boltzmann model for the nonlinear thermistor equations

Abstract

In this paper, we propose a general and efficient lattice Boltzmann (LB) model for solving the nonlinear thermistor equations, where the nonlinear diffusion and Poisson equations are solved by two LB equations. Through Chapman–Enskog analysis, the nonlinear thermistor equations can be recovered correctly from the present LB model. We then test the model through some numerical simulations, and find that the numerical results are in good agreement with analytical solutions. Additionally, the numerical results also show that the present LB model has a second-order convergence rate in space.