稀薄流到连续流的气体运动论统一数值算法初步研究

从非线性模型Ｂｏｌｔｚｍａｎｎ方程出发，引入简化速度分布函数、使用离散速度坐标法对速度空间进行离散、降维，去掉分布函数对速度分量的连续依赖性；采用时间分裂法，将简化速度分布函数松驰变化方程分解为源项碰撞变化方程、对流运动方程，进行耦合计算，应用ＮＮＤ耗散差分方法直接模拟气体分子速度分布函数；发展离散速度数值积分法，通过宏观取矩获取物理空间各点的流动参数，从而建立一套能有效模拟各流域气动问题的简化的

Study on Gas Kinetic Algorithm for Flows from Rarefied Transition to Continuum

Based on the nonlinear Boltzmann model equation, the unified simplified velocity distribution function equations adapted to various flow regimes can be presented. The discrete ordinate method is applied to the reduced distribution functions in order to replace their continuous dependency on the velocity space, and then the kinetic model equation will be cast into hyperbolic conservation laws form with nonlinear source terms. The time splitting method is used to split the distribution function equations into the colliding relaxation equation and the convection movement equations. The NND finite difference method is adopted and extended to solve them. To improve computational efficiency for various Mach number flows, three types of quadrature rules are used to evaluate the macroscopic flow parameters at each point in the physical space. As a result, a simplified unified kinetic algorithm for the gas dynamical problems from various flow regimes has been developed. The computations of the one dimensional shock tube problem and the flows over two dimensional circular cylinder from rarefied transition to continuum indicate that both high resolution of the flow fields and good qualitative agreement with the theoretical, DSMC and experimental results can be obtained.