中文摘要：

同伦分析方法（homotopy analysis method,HAM）是求解强非线性问题的有力手段.针对颗粒流的动理学理论中的非线性微分积分方程——Boltzmann方程,采用HAM方法选取局域Maxwell速度分布函数作为初始猜测解,得到了低浓度颗粒流的Boltzmann方程的一阶近似解,与传统的Chapman-Enskog方法得到的一阶近似解表达式的结构一致,初步显示了HAM方法求解Boltzmann方程的有效性,为一般Boltzmann方程的HAM方法求解奠定了基础.

英文摘要：

Homotopy analysis method is a new and efficient way to nonlinear problems. The nonlinear Boltzmann equation with differential and integral terms is discussed. The local Maxwell velocity distribution function is chosen as the initial conjecture solution in the Boltzmann equation of dilute granular flow. The concrete expression of the first-order approximate solution to Boltzmann equation with collision term being BGK model, which is consistent to the solution by Chapman-Enskog method, is given. It does not rely on little parameters. It is a successful application of HAM and the base of solving more general Boltzmann equation in the feature.