从稀薄流到连续流的统一数值算法研究

In this study, it's to be considered whether a unified numerical algorithm to predict the gas flows over the complete spectrum of flow regimes can be found. Based on the modified BGK model equation, the unified simplified velocity distribution function equation.adapted to various flow regimes can be presented by introducing the simplified velocity distribution functions with the aid of the basic characteristics on molecular movement and collision approaching to equilibrium. The discrete velocity ordinate method in the kinetic theory of gases is developed and applied to discretize the corresponding velocity components, and then the molecular velocity distribution function equation will be cast into hyperbolic conservation.laws form with nonlinear source terms. In view of the unsteady characteristic of molecular convective movement and colliding relaxation, the time-splitting method is applied to decompose the velocity distribution function equations into the colliding relaxation equations with nonlinear.source terms and the convective motion equations. Based on the second-order Runge-Kutta method and the non-oscillatory, containing no free parameters, and dissipative (NND) finite difference method, the gas kinetic finite difference second-order scheme is constructed to directly.solve the discrete velocity distribution functions. The discrete velocity numerical quadrature rules,.such as the modified Gauss-Hermite formula, the Newton-Cotes composite integration method and the Gauss-Legendre numerical quadrature rule, are developed and applied to evaluate the macroscopic flow moments of the distribution functions over the velocity space. As a result, a unified gas kinetic algorithm is established for the flows from rarefied transition to continuum regime. To test the reliability of the present method, the one-dimensional shock wave structures,.the flows past two-dimensional circular cylinder and the three-dimensional flows over sphere withvarious Knudsen numbers are simulated. The computational results are found in high resolution of the flow fields and good qualitative agreement with the theoretical, DSMC, and experimental.results

本项目从Boltzmann方程出发，引入合理的简化，建立含流态控制参数的从稀薄流到连续统坏钠宸肿铀俣确植己刂品匠蹋皇褂糜庞贛onte Carlo积分的黄金分割法，完成有关积分和对速度坐标的离散，使方程降维，然后应用无波动、无自由参数的差分方法数值模拟离散、降维的气体分子速度分布函数方程，并进一步通过黄金分割积分法，获取各流域宏观流动参数，从而建立一套从稀薄流到连续流统一的气体运动论数值算法。