A lattice Bhatnagar--Gross--Krook model for a class of the generalized Burgers equations

A new lattice Bhatnagar--Gross--Krook (LBGK) model for a class of the generalizedBurgers equations is proposed. It is a general LBGK model for nonlinear Burgersequations with source term in arbitrary dimensional space. The linear stability ofthe model is also studied. The model is numerically tested for three problems indifferent dimensional space, and the numerical results are compared with eitheranalytic solutions or numerical results obtained by other methods. Satisfactoryresults are obtained by the numerical simulations.