A new lattice Boltzmann model for solving the coupled viscous Burgers' equation

In this paper, a new lattice Boltzmann model for the coupled nonlinear system of viscous Burgers' equation is proposed by using the double evolutionary equations. Through selecting equilibrium distribution functions and amending functions properly, the governing evolution system can be recovered correctly according to our proposed scheme, in which the Chapman-Enskog expansion is employed. The effects of space and time resolutions on the accuracy and stability of the model are numerically investigated in detail. The numerical solutions for various initial and boundary conditions are calculated and validated against analytic solutions or other numerical solutions reported in previous studies. It is found that the numerical results agree well with the analytic solutions, which indicates the potential of the present algorithm for solving the coupled nonlinear system of viscous Burgers' equation.