一类含源Boussinesq系统解的数值分析及仿真

Abstract

For a class of initial value problems of the high-order Boussinesq systems with source terms, a D1Q5 nonstandard lattice Boltzmann model (LBM) with correction functions and source terms was proposed. Different local equilibrium distribution functions and correction functions were selected, and the nonlinear wave equation was recovered by means of the Chapman-Enskog multi-scale analysis and the Taylor expansion technique. Some initial boundary value problems of the Boussinesq systems with analytical solutions were simulated to verify the effectiveness of the LBM. The results show that the numerical solutions agree well with the analytical solutions and the norm errors obtained with the LBM are smaller than those with the modified finite difference method (MFDM). Furthermore, some problems without analytical solutions were numerically studied with the present method and the MFDM. The comparison shows that the numerical solutions from the LBM are in good agreement with those from the MFDM, which validates the effectiveness and stability of the proposed model.