基于线性化动力学方程的微流动数值模拟统一气体动力学格式
A Unified Gas-kinetic Scheme for Micro Flow Simulation Based on Linearized Kinetic Equation
摘要：
根据努森数的不同，微流体的流动状态可以从无碰撞状态过渡到流体动力状态。在动力学尺度上，微流体的动力学行为可用线性化的动力学方程描述。在连续区域，流体动力学方程，如线性化的纳维-斯托克斯方程和欧拉方程可以通过Chapman-Enskog渐近分析从线性化的动力学方程导出。本文基于线性化的动力学方程，提出了一种适用于微流场模拟的统一气体动力学格式（UGKS），它是一种适用于整个微流场的多尺度格式。UGKS的重要方法如下。首先，将微观分布函数的演化与宏观流量的演化耦合起来。其次，基于动力学方程的积分解构造了UGKS的数值通量，提供了一个真正的多尺度、多维的数值通量。UGKS恢复的线性动力学解决方案在稀薄的制度，并收敛到线性流体动力学解决方案在连续的制度。UGKS的一个突出特点是即使当网格尺寸远大于动力学长度尺度时也能捕获精确的粘性解，例如捕获网格尺寸为颗粒平均自由程10倍的粘性边界层，这种多尺度性质被称为统一保持（UP），在\cite{guo2019unified}中已经研究过。本文还对UGKS的UP性质给出了数学证明。
英文摘要：
The flow regime of micro flow varies from collisionless regime to hydrodynamic regime according to the Knudsen number. On the kinetic scale, the dynamics of micro flow can be described by the linearized kinetic equation. In the continuum regime, hydrodynamic equations such as linearized Navier-Stokes equations and Euler equations can be derived from the linearized kinetic equation by the Chapman-Enskog asymptotic analysis. In this paper, based on the linearized kinetic equation we are going to propose a unified gas kinetic scheme scheme (UGKS) for micro flow simulation, which is an effective multiscale scheme in the whole micro flow regime. The important methodology of UGKS is the following. Firstly, the evolution of microscopic distribution function is coupled with the evolution of macroscopic flow quantities. Secondly, the numerical flux of UGKS is constructed based on the integral solution of kinetic equation, which provides a genuinely multiscale and multidimensional numerical flux. The UGKS recovers the linear kinetic solution in the rarefied regime, and converges to the linear hydrodynamic solution in the continuum regime. An outstanding feature of UGKS is its capability of capturing the accurate viscous solution even when the cell size is much larger than the kinetic kinetic length scale, such as the capturing of the viscous boundary layer with a cell size ten times larger than the particle mean free path. Such a multiscale property is called unified preserving (UP) which has been studied in \cite{guo2019unified}. In this paper, we are also going to give a mathematical proof for the UP property of UGKS.
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。
