非平衡气体动力学的建模和计算:超越单一松弛时间动力学模型

Xiaocong Xu, Yipei Chen, K. Xu
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引用次数: 21

摘要

非平衡气体动力学用玻尔兹曼方程来描述,该方程可以通过确定性和随机方法进行数值求解。由于玻尔兹曼方程的碰撞项比较复杂,在过去的70年里,人们提出了许多动力学松弛模型并应用于稀薄流动的研究。为了发展稀薄连续流模拟的多尺度方法,采用动力学模型方程的积分解,建立了dvm型统一气体动力学格式(UGKS)。UGKS在单元尺寸和时间步长尺度上模拟气体动力学,同时在一个时间步长范围内考虑了粒子输运和碰撞的累积效应。在UGKS框架下,进一步发展了用于非平衡流动模拟的统一气动波粒(UGKWP)方法,其中气体分布函数的时间演化由解析波和单个粒子组成。在高度稀薄状态下,粒子输运和碰撞将起主导作用。由于粒子碰撞的单一松弛时间模型,UGKWP解与完全玻尔兹曼或DSMC结果之间存在明显的差异,特别是在高马赫和克努森数情况下。在本文中,除了动力学松弛模型外,还将在UGKWP中实现粒子碰撞时间根据粒子速度的修正。结果表明,该模型极大地提高了UGKWP捕获非平衡流的性能。在高度稀薄的状态下,UGKWP与DSMC或玻尔兹曼解是完美匹配的。在近连续和连续流动状态下,在小单元Knudsen数下,UGKWP将逐渐回归到基于宏观变量的Navier-Stokes流解。
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Modeling and computation for non-equilibrium gas dynamics: Beyond single relaxation time kinetic models
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.
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