自由冷却稀颗粒气体中的密度爆破：流体动力学与分子动力学
Attempted density blowup in a freely cooling dilute granular gas: hydrodynamics versus molecular dynamics
摘要：
最近的研究表明（Fouxon等人，2007），在理想颗粒流体动力学（IGHD）的框架中，颗粒气体的初始光滑流体动力学流动可以在有限时间内产生无限大的气体密度。表现出这种性质的精确解已经推导出来。在奇点附近，颗粒气体的压力是有限的，几乎是常数。这项工作报告的分子动力学（MD）模拟的自由冷却气体的几乎弹性碰撞硬盘，旨在确定“企图”密度爆破制度。模拟流的初始条件模仿IGHD方程的一个特定的解决方案，表现出密度爆破。我们在MD模拟中测量流体动力学场，并将其与理想理论的预测进行比较。我们发现一个显着的定量之间的协议在一个较长的时间间隔，证明存在的企图爆破制度。当试图接近奇点时，在MD模拟中观察到的流体动力学场偏离理想解的预测。为了研究奇点附近理想理论的崩溃机制，我们分别考虑梯度相关的运输和有限密度修正，扩展了流体动力学理论。
英文摘要：
It has been recently shown (Fouxon et al. 2007) that, in the framework of ideal granular hydrodynamics (IGHD), an initially smooth hydrodynamic flow of a granular gas can produce an infinite gas density in a finite time. Exact solutions that exhibit this property have been derived. Close to the singularity, the granular gas pressure is finite and almost constant. This work reports molecular dynamics (MD) simulations of a freely cooling gas of nearly elastically colliding hard disks, aimed at identifying the "attempted" density blowup regime. The initial conditions of the simulated flow mimic those of one particular solution of the IGHD equations that exhibits the density blowup. We measure the hydrodynamic fields in the MD simulations and compare them with predictions from the ideal theory. We find a remarkable quantitative agreement between the two over an extended time interval, proving the existence of the attempted blowup regime. As the attempted singularity is approached, the hydrodynamic fields, as observed in the MD simulations, deviate from the predictions of the ideal solution. To investigate the mechanism of breakdown of the ideal theory near the singularity, we extend the hydrodynamic theory by accounting separately for the gradient-dependent transport and for finite density corrections.
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