基于模型方程解析解的跨流域流动数值方法研究

Flow embracing various regimes is a general phenomenon during the vehicle flight in the nearspace.In order to solve this type of flow efficiently, people usually construct a hybrid algorithm by coupling two different solvers , one for the continuum flow regime and the other for the rarefied regime,such as the widely used DSMC/NS hybrid algorithm.Currently,in most hybrid algorithms, the two basic solvers are intrinsically of different type, which results in much difficulties in the message exchange at the interfaces. Meanwhile,the so-called BGK-NS scheme which is equivalent to solving the Navier-Stokes equations and UGKS scheme for all flow regimes can be constructed based on the analytic solution of the Boltzmann model equation, pointing a new way for a hybrid algorithm.The aim of this proposal is to program the BGK-NS and UGKS scheme. Then the original UGKS scheme will be modified in the implementation of the collision term and the velocity space adaption will be introduced in order to improve the efficiency and preciseness. Finally, a hybrid algorithm based on the Boltzmann model equation will be constructed and applied in the complex flow induced by the interaction between the rarefied freestream and the continumm jet.

飞行器在临近空间领域时，跨流域流动现象非常普遍。考虑到计算效率，研究者通常需要将稀薄流求解器和连续流求解器采用某种方式耦合起来构造混合方法，如DSMC/NS混合方法。目前多数混合方法中的两类求解器具有不同的性质，因而在两种方法的交界面上信息传递存在诸多问题。而从Boltzmann模型方程出发，借助于解析解，可以分别构造等价于求解NS方程的BGK-NS算法以及适用于全流域求解的统一算法（UGKS）。这为我们构造本质一致的混合算法提供了一种新的思路。本项目的目的是建立BGK-NS以及UGKS算法，并针对UGKS中随离散速度坐标法的引入而带来的额外计算量，从碰撞项积分处理方法以及相空间网格自适应等方面对该算法进行改造，提高计算效率，增加算法的严谨性。在此基础上，构造BGK-NS/UGKS混合算法，并在高空高超声速条件下侧向喷流与来流的干扰这一复杂而典型的跨流域流动现象上进行初步应用。

本项目建立了BGK-NS以及UGKS算法，并针对UGKS中随离散速度坐标法的引入而带来的额外计算量，从碰撞项积分处理方法以及相空间网格自适应等方面对该算法进行改造，提高计算效率，增加算法的严谨性。采用LU分解求解模型方程，实现了隐式UGKS。完成了三维圆球和NASA的X38飞行器跨流域绕流的模拟。在此基础上，构造BGK-NS/UGKS混合算法，并在高空高超声速条件下侧向喷流与来流的干扰这一复杂而典型的跨流域流动现象上进行初步应用。