论文标题
非平衡气体动力学的建模和计算：超越动力学弛豫模型
Modeling and computation for non-equilibrium gas dynamics: beyond kinetic relaxation model
论文作者
论文摘要
非平衡气体动力学由玻尔兹曼方程描述，可以通过确定性和随机方法来数值求解。由于Boltzmann方程的复杂碰撞项，在过去的70年中，已经提出并使用了许多动力学弛豫模型，用于研究稀有流动。为了通过采用动力学模型方程的积分解决方案来开发用于稀有和连续流仿真的多尺度方法，已经构建了DVM型统一气体运动方案（UGK）。 UGK模拟了电池尺寸和时间步骤尺度上的气体动力学，而粒子传输和碰撞的累积效应已在一个时间步长中考虑到。在UGK框架下，已经进一步开发了用于非平衡流量模拟的统一气体波动粒子（UGKWP）方法，其中气体分布函数的时间演变由分析波和个体粒子组成。在高度稀有的制度中，粒子运输和碰撞将起主要作用。由于粒子碰撞的单个松弛时间模型，UGKWP解决方案与完整的Boltzmann或DSMC结果之间存在明显的差异，尤其是在高马赫和Knudsen数字的情况下。在本文中，除了动力学松弛模型外，根据粒子速度的粒子碰撞时间的修改还将在UGKWP中实现。结果，新模型大大提高了UGKWP在捕获非平衡流量中的性能。在高度稀有的政权中，UGKWP和DSMC或Boltzmann解决方案之间存在完美的匹配。在近连续和连续流程中，UGKWP将逐渐回到基于宏观变量的Navier-Stokes流量求解器，在小细胞knudsen编号处。
The non-equilibrium gas dynamics is described by the Boltzmann equation, which can be solved numerically through the deterministic and stochastic methods. Due to the complicated collision term of the Boltzmann equation, many kinetic relaxation models have been proposed and used in the past seventy years for the study of rarefied flow. In order to develop a multiscale method for the rarefied and continuum flow simulation, by adopting the integral solution of the kinetic model equation a DVM-type unified gas-kinetic scheme (UGKS) has been constructed. The UGKS models the gas dynamics on the cell size and time step scales while the accumulating effect from particle transport and collision has been taken into account within a time step. Under the UGKS framework, a unified gas-kinetic wave-particle (UGKWP) method has been further developed for non-equilibrium flow simulation, where the time evolution of gas distribution function is composed of analytical wave and individual particle. In the highly rarefied regime, particle transport and collision will play a dominant role. Due to the single relaxation time model for particle collision, there is a noticeable discrepancy between the UGKWP solution and the full Boltzmann or DSMC result, especially in the high Mach and Knudsen number cases. In this paper, besides the kinetic relaxation model, a modification of particle collision time according to the particle velocity will be implemented in UGKWP. As a result, the new model greatly improves the performance of UGKWP in the capturing of non-equilibrium flow. There is a perfect match between UGKWP and DSMC or Boltzmann solution in the highly rarefied regime. In the near continuum and continuum flow regime, the UGKWP will gradually get back to the macroscopic variables based Navier-Stokes flow solver at small cell Knudsen number.
