高速可压缩流的格子BGK动力学模型：流体动力学和非平衡行为
Lattice BGK kinetic model for high speed compressible flows: hydrodynamic and nonequilibrium behaviors
摘要：
本文提出了一种简单而通用的方法来建立高速可压缩流动的格点BGK模型。主要内容包括两个部分：一个合适的离散平衡分布函数（DEDF）$\mathbf{f}^{eq}$和一个具有灵活速度大小的离散速度模型。DEDF由$\mathbf{f}^{eq}=\mathbf{C}^{-1}\mathbf{M}$获得，其中$\mathbf{M}$是麦克斯韦分布函数的矩的集合，并且$\mathbf{C}$是连接DEDF和矩的矩阵。$\mathbf{C}$的数值分量由离散速度模型确定。$\mathbf{C}^{-1}$的计算是基于解析解，该解析解是控制离散速度大小的参数的函数。离散速度模型的选择具有很高的灵活性。该系统的比热容比可以是灵活的。该方法适用于一维，二维和三维模型的建设。作为一个例子，我们构造了一个新的格子BGK动力学模型，它不仅可以在连续极限恢复纳维-斯托克斯方程，而且可以测量系统偏离热力学平衡的程度。通过调整离散速度的大小，稳定模拟的马赫数可以显著增加到30甚至更高。该模型通过著名的基准测试进行了验证和确认。给出了系统在激波界面附近偏离热力学平衡时的一些宏观行为。
英文摘要：
We present a simple and general approach to formulate the lattice BGK model for high speed compressible flows. The main point consists of two parts: an appropriate discrete equilibrium distribution function (DEDF) $\mathbf{f}^{eq}$ and a discrete velocity model with flexible velocity size. The DEDF is obtained by $\mathbf{f}^{eq}=\mathbf{C}^{-1}\mathbf{M}$, where $\mathbf{M}$ is a set of moment of the Maxwellian distribution function, and $\mathbf{C}$ is the matrix connecting the DEDF and the moments. The numerical components of $\mathbf{C}$ are determined by the discrete velocity model. The calculation of $\mathbf{C}^{-1}$ is based on the analytic solution which is a function of the parameter controlling the sizes of discrete velocity. The choosing of discrete velocity model has a high flexibility. The specific heat ratio of the system can be flexible. The approach works for the one-, two- and three-dimensional model constructions. As an example, we compose a new lattice BGK kinetic model which works not only for recovering the Navier-Stokes equations in the continuum limit but also for measuring the departure of system from its thermodynamic equilibrium. Via adjusting the sizes of the discrete velocities the stably simulated Mach number can be significantly increased up to 30 or even higher. The model is verified and validated by well-known benchmark tests. Some macroscopic behaviors of the system due to deviating from thermodynamic equilibrium around the shock wave interfaces are shown.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
