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.针对两相流动理学理论中的非线性微分积分方程——Boltzmann方程,本文采用HAM方法选取Maxwell速度分布函数作为初始猜测解,求解得到了低浓度固液两相流的BGK模型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,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 in the kinetic theory of dilute solid-liquid two-phase flows is discussed.The local Maxwell velocity distribution function is chosen as the initial conjecture solution in the Boltzmann equation.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 is a successful application of HAM and the base of solving more general Boltzmann equation in the feature.