General propagation lattice Boltzmann model for a variable-coefficient compound KdV-Burgers equation

Abstract

• General propagation lattice Boltzmann model for vc-cKdVB equation is derived. • Chapman–Enskog analysis is given to recover vc-cKdVB equation from our model. • Effects of the free parameters induced in our model are discussed in detail. • Numerical results agree well with analytical solutions. • Our model could be more stable and more accurate than the standard model. In this paper, a general propagation lattice Boltzmann model for a variable-coefficient compound Korteweg-de Vries-Burgers (vc-cKdVB) equation is investigated through selecting equilibrium distribution function and adding a compensation function, which can provide some more realistic models than their constant-coefficient counterparts in fluids or plasmas. Chapman–Enskog analysis shows that the vc-gKdVB equation can be recovered correctly from the present model. Numerical simulations in different situations of this equation are conducted, including the propagation and interaction of the bell-type, kink-type and periodic-depression solitons and the evolution of the shock-wave solutions. It is found that the numerical results match well with the analytical solutions, which demonstrates that the current lattice Boltzmann model is a satisfactory and efficient algorithm. In addition, it is also shown the present model could be more stable and more accurate than the standard lattice Bhatnagar–Gross–Krook model through adjusting the two free parameters introduced into the propagation step.