格子Boltzmann方法解扩散方程的复杂边界条件研究  

On Complex Boundary Conditions of the Lattice Boltzmann Method for the Diffusion Equations

作　　者：黄俊涛[1,2] 张力[1] 雍稳安 王沫然[1] 

机构地区：[1]清华大学航天航空学院工程力学系,北京100084 [2]清华大学周培源应用数学研究中心,北京100084

出　　处：《应用数学和力学》2014年第3期305-312,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(51176089);国家重点基础研究发展计划(973计划)(2013CB228301)~~

摘　　要：对格子Boltzmann方法求解含第三类边界条件的扩散方程进行了理论和数值研究,构造了一种新的基于bounce-back的边界处理数值格式,用来处理复杂边界问题.借助渐近分析,证明了新方法的数值相容性.用数值算例从不同角度分析了算法的精度和稳定性等,与已有算法相比,新方法在精度、稳定性和效率方面均有较大提高.最后通过一个复杂边界反应扩散的示例演示了新方法应用于复杂多孔介质内多物理化学输运模拟的可行性和有效性.The diffusion equation with the third-type boundary condition solved by the lattice Boltzmann method was theoretically and numerically studied. A new numerical algorithm based on the bounce-back method was constructed, to deal with the complex boundary problem. By asymptotic analysis, the compatibility of the numerical method was proved. The accuracy and stability of the algorithm were discussed via several numerical examples. Compared with the previous work, this numerical approach makes a significant improvement in the aspects of ac- curacy, stability and efficiency. Finally, through the numerical example of a reaction-diffusion problem with complex boundary, feasibility and effectiveness of the presented method are proved in the simulation of the multi-physical and chemical transport process in porous medi- um.

关 键 词：格子BOLTZMANN方法 扩散方程 第三类边界条件 渐近分析 复杂边界 

分 类 号：O242.5[理学—计算数学] O357.3[理学—数学]