应用格子Boltzmann模型模拟一类二维偏微分方程  

Use of lattice Boltzmann method to simulate 2-D partial differential equation

作　　者：何郁波[1] 林晓艳[1] 董晓亮[2] 

机构地区：[1]怀化学院数学系,怀化418008 [2]北方民族大学信息与计算科学学院,银川750021

出　　处：《物理学报》2013年第19期282-288,共7页Acta Physica Sinica

基　　金：湖南省教育厅重点项目(批准号:08A503);湖南省教育厅青年骨干教师和国内访问学者基金(批准号:湘教通[2012]510号)资助的课题~~

摘　　要：针对一类含源的二维非线性偏微分方程,通过Chapman-Enskog展开技术和多尺度分析提出了带修正项的简单格子Boltzmann模型.用模型模拟了几类二维偏微分方程,数值模拟结果与精确解相符合.成功将格子Boltzmann方法应用到二维偏微分方程的数值求解中.For a class of two-dimensional nonlinear partial differential equation with the source term,a simple lattice Boltzmann model with amending function is proposed and studied using the Chapman-Enskog expansion technique and multiple-scale analysis. In this paper, some partial differential equation are simulated, the numerical results and exact solutions are shown to be almost completely fitting with each other. The lattice Boltzmann method is further extended to two-dimensional partial differential equation.

关 键 词：二维非线性偏微分方程 格子BOLTZMANN模型 Chapman—Enskog多尺度展开 

分 类 号：O175.2[理学—数学]