变系数反应扩散方程的格子Boltzmann模型

Lattice Boltzmann model for reaction-diffusion equation with variable coefficient

摘要: 研究了含变系数的反应扩散方程,构建了含弛豫时间函数τ(x,t)的D1Q3格子Boltzmann模型.为了能准确地恢复出此宏观方程,利用Chapman-Enskog展开和多尺度分析技术,推导出了各个方向的平衡态分布函数和弛豫时间函数τ(x,t)的具体表达式.数值计算结果表明该模型是稳定、有效的.

Abstract: The reaction-diffusion equation with variable coefficient is investigated.And the D1Q3 lattice Boltzmann model with relaxation time function τ(x,t) is developed to numerically solve the equation.In order to recover the governing equation correctly,based on the Chapman-Enskog expansion and multi-scale technique,the specific expression of equilibrium distribution function and relaxation time function are deduced.The numerical computation results show that the D1Q3 lattice Boltzmann model is stable and effective.