Yang L M, Li Z H, Shu C, Liu Y Y, Liu W, Wu J
State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
MIIT Key Laboratory of Unsteady Aerodynamics and Flow Control, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
Phys Rev E. 2023 Jul;108(1-2):015302. doi: 10.1103/PhysRevE.108.015302.
This work proposes a discrete unified gas-kinetic wave-particle (DUGKWP) method for simulation of flows in all flow regimes. Unlike the discrete velocity method (DVM) and the direct simulation Monte Carlo (DSMC) method which solve the governing equations by either the deterministic method or the stochastic method, the DUGKWP combines the advantages of these two methods. In the DUGKWP, the information of microscopic particles as well as macroscopic flow variables are both evolved. Specifically, the microscopic particles are updated by the free-transport and resampling processes, while the macroscopic flow properties are evolved via solving the macroscopic governing equations of conservation laws with the finite volume method. According to the discrete characteristic solution to the Boltzmann-BGK equation utilized in the DUGKWP, in the highly rarefied flow regime, the motion of microscopic particles greatly determines the fluxes for the macroscopic governing equations. Conversely, for the continuum flow, no microscopic particle exists in the computational domain and the DUGKWP is degraded to the Navier-Stokes solver. Numerical studies validate that the DUGKWP can accurately predict the flow properties in all flow regimes. Furthermore, compared with the deterministic method, the DUGKWP enjoys superior efficiency with less memory consumption for both high-speed rarefied flows and flows close to the continuum regime.
本文提出了一种离散统一气体动力学波粒（DUGKWP）方法，用于模拟所有流动状态下的流动。与通过确定性方法或随机方法求解控制方程的离散速度方法（DVM）和直接模拟蒙特卡罗（DSMC）方法不同，DUGKWP结合了这两种方法的优点。在DUGKWP中，微观粒子的信息以及宏观流动变量都在演化。具体而言，微观粒子通过自由传输和重采样过程进行更新，而宏观流动特性则通过有限体积法求解守恒定律的宏观控制方程来演化。根据DUGKWP中使用的玻尔兹曼 - BGK方程的离散特征解，在高度稀薄流动状态下，微观粒子的运动极大地决定了宏观控制方程的通量。相反，对于连续介质流动，计算域中不存在微观粒子，DUGKWP退化为纳维 - 斯托克斯求解器。数值研究验证了DUGKWP能够准确预测所有流动状态下的流动特性。此外，与确定性方法相比，DUGKWP在高速稀薄流动和接近连续介质状态的流动中都具有更高的效率和更少的内存消耗。
