Nonlinear analysis of the shearing instability in granular gases
Nonlinear analysis of the shearing instability in granular gases
复制标题
颗粒气体剪切不稳定性的非线性分析
DOI：
10.1103/physreve.62.3836
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
Malek Mansour M
中科院分区：
文献类型：
--
作者：
Soto;Mareschal;Malek Mansour M
众所周知，当耗散超过一个阈值时，有限尺寸的均匀颗粒流体会产生类似流体动力学的不稳定性。这种不稳定性进行了分析，在修改后的流体动力学方程：首先，源项被添加到能量方程，占碰撞时的能量耗散和现象学的傅立叶定律是根据以前的结果概括。第二，重新标度的时间形式主义的介绍，映射到一个非平衡稳态的均匀冷却状态。一个非线性稳定性分析所得到的方程进行预测的外观的流动模式。产生了密度和温度的稳定调制，这不会导致聚类。此外，获得了一个全球性的温度下降，引起的碰撞频率和耗散率的下降。良好的协议与分子动力学模拟的非弹性硬盘被发现为低耗散。
It is known that a finite-size homogeneous granular fluid develops a hydrodynamiclike instability when dissipation crosses a threshold value. This instability is analyzed in terms of modified hydrodynamic equations: first, a source term is added to the energy equation which accounts for the energy dissipation at collisions and the phenomenological Fourier law is generalized according to previous results. Second, a rescaled time formalism is introduced that maps the homogeneous cooling state into a nonequilibrium steady state. A nonlinear stability analysis of the resulting equations is done which predicts the appearance of flow patterns. A stable modulation of density and temperature is produced that does not lead to clustering. Also a global decrease of the temperature is obtained, giving rise to a decrease of the collision frequency and dissipation rate. Good agreement with molecular dynamics simulations of inelastic hard disks is found for low dissipation.