An analytical solution to Boltzmann equation of dilute granular flow with homotopy analysis method  

作　　者：ZHANG Li WANG GuangQian FU XuDong SUN QiCheng 

机构地区：[1]School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410075, China [2]State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China

出　　处：《Chinese Science Bulletin》2009年第23期4365-4370,共6页

基　　金：Supported by the National Basic Research Program of China (Grant No. 2007CB714101);Research Fund of the State Key Laboratory for Hydroscience and Engineering in Tsinghua University (Grant No. 2008-ZY-6)

摘　　要：The homotopy analysis method (HAM), as a new mathematical tool, has been employed to solve many nonlinear problems. As a fundamental equation in non-equilibrium statistical mechanics, the Boltzmann integro-differential equation (BE) describing the movement of particles is of strong nonlinearity. In this work, HAM is preliminarily applied to dilute granular flow which is relatively simple. By choosing the Maxwell velocity distribution function as the initial solution, the concrete expression of the first-order approximate solution to BE with collision term being the BGK model is given. Furthermore it is consistent with the solution using Chapman-Enskog method but does not rely on little parameters.The homotopy analysis method （HAM）, as a new mathematical tool, has been employed to solve many nonlinear problems. As a fundamental equation in non-equilibrium statistical mechanics, the Boltzmann integro-differential equation （BE） describing the movement of particles is of strong nonlinearity. In this work, HAM is preliminarily applied to dilute granular flow which is relatively simple. By choosing the Maxwell velocity distribution function as the initial solution, the concrete expression of the first-order approximate solution to BE with collision term being the BGK model is given. Furthermore it is consistent with the solution using Chapman-Enskog method but does not rely on little parameters.

关 键 词：颗粒流 玻尔 流方程 稀释 积分微分方程 速度分布函数 非线性问题 一阶近似解 

分 类 号：O413.1[理学—理论物理] TQ021.1[理学—物理]