A lattice Boltzmann model for the Korteweg–de Vries equation with two conservation laws

A lattice Boltzmann model for the Korteweg–de Vries (KdV) equation is presented by using the higher-order moment method. In contrast to the previous lattice Boltzmann model to the KdV equation, our method has higher-order accuracy. Two key steps in the development of this model are the addition of a momentum conservation condition, and the construction of a correlation between the first conservation law and the second conservation law. The numerical example shows the higher-order moment method can be used to raise the truncation error of the lattice Boltzmann scheme.