Lattice Boltzmann model for a class of coupled nonlinear partial differential equations with variable coefficients

In this paper, a unified lattice Boltzmann model is proposed for a class of coupled nonlinear partial differential equations with variable coefficients. To deal with variable coefficients and coupling problems in equations, the scheme uses part of the convective terms as source terms and rewrites the coupled partial differential equations into a general equation. Through selecting equilibrium distribution functions and amending functions properly, the macroscopic equations with the second order accuracy can be recovered correctly from the Lattice Boltzmann model. Some numerical experiments are used to validate the model, and the numerical results agree well with the analytical solutions, indicating that the current lattice Boltzmann model is an effective method for solving a class of coupled nonlinear partial differential equations with variable coefficients.