摘要
针对一维热扩散方程的数学特点,建立了热扩散方程离散速度模型,构造了其平衡态分布函数,采用Chapman-Enskog展开和多尺度技术,构建了用于求解一维热扩散方程的D1Q3模型,进行了验证性数值实验。实验结果表明,模型的数值解与文献的解析解吻合良好,其两者的误差随网格细化而大幅度减小,从而说明了本文构建的格子Boltzmann模型可用于求解一维热扩散方程。
According to the mathematical characteristics of one dimension thermal diffusion equation, the discrete velocity model and an equilibrium distribution function of thermal diffusion equation were established. D1 Q3 model was proposed for one dimension thermal diffusion equation using Chapman - Enskog expansion and muhiscale technique. Verification experiments were conducted. The results show that the simulation results are consistent with analytic solutions. The absolute errors between the simulation and analytic solutions become smaller with the mesh refining. And the effectiveness of the lattice Bohzmann model to solve one dimension thermal diffusion equation in this paper is verified.
出处
《节能技术》
CAS
2015年第3期199-202,共4页
Energy Conservation Technology
基金
国家自然科学基金(No.51274071)
