A lattice Boltzmann model for the generalized Burgers–Huxley equation

In this paper we develop a lattice Boltzmann model for the generalized Burgers–Huxley equation (GBHE). By choosing the proper time and space scales and applying the Chapman–Enskog expansion, the governing equation is recovered correctly from the lattice Boltzmann equation, and the local equilibrium distribution functions are obtained. Excellent agreement with the exact solution is observed, and better numerical accuracy is obtained than the available numerical result. The results indicate the present model is satisfactory and efficient. The method can also be applied to the generalized Burgers–Fisher equation and be extended to multidimensional cases.