标题： 慢非等温流动：玻尔兹曼方程的数值和渐近分析 显示英文标题

标题： Slow nonisothermal flows: numerical and asymptotic analysis of the Boltzmann equation

摘要： 在高热应力下，稀薄气体的缓慢流动被考虑。 这类流动的正确流体力学描述基于Kogan--Galkin--Friedlander方程，在动量方程中包含了一些非纳维-斯托克斯项。 适当的边界条件通过基于玻尔兹曼方程的克努森层渐近分析确定。 研究了至克努森数二阶的边界条件。 对一些二维例子进行了比较分析。 流体力学结果得到了通过Tcheremissine的投影插值离散速度方法扩展用于非均匀网格后求得的玻尔兹曼方程数值解的支持。 首次获得了第一阶和第二阶非线性热应力流动之间的竞争模式。 显示英文摘要

摘要： Slow flows of a slightly rarefied gas under high thermal stresses are considered. The correct fluid-dynamic description of this class of flows is based on the Kogan--Galkin--Friedlander equations, containing some non-Navier--Stokes terms in the momentum equation. Appropriate boundary conditions are determined from the asymptotic analysis of the Knudsen layer on the basis of the Boltzmann equation. Boundary conditions up to the second order of the Knudsen number are studied. Some two-dimensional examples are examined for their comparative analysis. The fluid-dynamic results are supported by numerical solution of the Boltzmann equation obtained by the Tcheremissine's projection-interpolation discrete-velocity method extended for nonuniform grids. The competition pattern between the first- and the second-order nonlinear thermal-stress flows has been obtained for the first time.