Abstract: The lattice Boltzmann model was used to solve a class of third order partial differential equations with variable coefficients and source terms. By using Chapman-Enskog expansion technology, the macroscopic equation with the third order accuracy was recovered by selecting appropriate equilibrium distribution function and compensation function. Numerical simulation results verify the effectiveness of the proposed model.

Key words: lattice Boltzmann method, Chapman-Enskog expansion, variable coefficient, third order partial differential equation