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Evolution of Shock Instability in Granular Gases with Viscoelastic Collisions

机译:粘弹性碰撞中粒状气体冲击不稳定的演变

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Shocks in granular media have been shown to develop instabilities. We address the role that early stages of shock development have on this type of instability. We look at the evolution of shock waves driven by a piston in a dilute system of smooth inelastic disks, using both discrete particle and continuum modelling. To mimic a realistic granular gas, viscoelastic collisions are approximated with an impact velocity threshold u~* needed for inelastic collisions to occur. We show that behaviour of the shock evolution is dependent on the ratio of piston velocity to impact velocity threshold u_p/u~*, and the coefficient of restitution ε. For u_p/u~* = 2.0, we recover shock evolution behaving similar to that observed in purely inelastic media. This is characterized by a short period where the shock front pulls towards the piston before attaining a developed structure. No pullback is seen for u_p/u~* = 1.0. Results show the onset of instability for these stronger shocks during this evolving stage. These results suggest that the early stages of shock evolution play an important role in the shock instability.
机译:已经显示粒度介质的冲击以发展不稳定。我们解决了震荡开发的早期阶段对这种不稳定性的作用。我们使用离散粒子和连续型造型来看由活塞在稀释系统中由活塞驱动的冲击波驱动的演变。为了模仿现实的颗粒气体,粘弹性碰撞近似用冲击速度阈值U〜*需要发生无弹性碰撞。我们表明,冲击进化的行为取决于活塞速度与冲击速度阈值U_P / U〜*的比率,以及恢复系数ε。对于u_p / u〜* = 2.0,我们恢复震动演进行为类似于在纯粹的内部介质中观察到的行为。这是在达到开发结构之前朝向活塞朝向活塞朝向活塞的短时间的特征在于短段。对于U_P / U〜* = 1.0,没有看到RUTERBACK。结果显示了在这种不断发展的阶段的这些更强冲击的不稳定发作。这些结果表明,冲击进化的早期阶段在休克不稳定中发挥着重要作用。

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