一类非线性偏微分方程的四阶格子Boltzmann模型

A fourth order lattice Boltzmann model for nonlinear partial differential equation

通过Chapman-Enskog展开技术和多尺度分析,建立了一种新的D1Q4带修正项的四阶格子Boltzmann模型,一类非线性偏微分方程从连续的Boltzmann方程得到正确恢复.统一了KdV和Burgers等已知方程类型的格子BGK模型,还首次给出了组合KdV-Burgers,广义Burgers-Huxley等方程的四阶LBGK模型.数值模拟结果表明了该模型的有效性和稳定性.

A new DIQ4 fourth order lattice Boltzmann model with amending function is presented for nonlinear partial differential equations. By using Chapman-Enskog expansion technique and multiple-scale analysis, a class of NPEs are restored correctly from continuous Boltzmann equation. This paper not only gives a unified lattice BGK model for the well-known equation such as KdV and Burgers equation, but also firstly gives a fourth order LBGK model for the combined KdV-Burgers equation, generalized Burgers-Huxley equation, etc. Numerical simulation results show that the method described in this paper is effective and stable.