Lattice Boltzmann method for the generalized Kuramoto–Sivashinsky equation

In this paper, a lattice Boltzmann model with an amending function is proposed for the generalized Kuramoto–Sivashinsky equation that has the form ut+uux+αuxx+βuxxx+γuxxxx=0ut+uux+αuxx+βuxxx+γuxxxx=0. With the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. It is found that the numerical results agree well with the analytical solutions.