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Kuwabara-Kono numerical dissipation: a new method to simulate granular matter
IMA Journal of Applied Mathematics ( IF 1.2 ) Pub Date : 2020-02-03 , DOI: 10.1093/imamat/hxz034
Guillaume James 1 , Kirill Vorotnikov 1 , Bernard Brogliato 1
Affiliation  

A new method is introduced for the simulation of multiple impacts in granular media using the Kuwabara-Kono (KK) contact model, a nonsmooth (not Lipschitz continuous) extension of Hertz contact that accounts for viscoelastic damping. We use the technique of modified equations to construct time-discretizations of the nondissipative Hertz law matching numerical dissipation with KK dissipation at different consistency orders. This allows us to simulate dissipative impacts with good accuracy without including the nonsmooth KK viscoelastic component in the contact force. This tailored numerical dissipation is developed in a general framework, for Newtonian dynamical systems subject to dissipative forces proportional to the time-derivative of conservative forces. Numerical tests are performed for the simulation of impacts in Newton’s cradle and on alignments of alternating large and small balls. Resulting wave phenomena (oscillator synchronization, propagation of dissipative solitary waves, oscillatory tails) are accurately captured by implicit schemes with tailored numerical dissipation, even for relatively large time steps.

中文翻译:

Kuwabara-Kono数值耗散:模拟颗粒物的新方法

引入了一种新的方法,用于使用Kuwabara-Kono(KK)接触模型模拟粒状介质中的多种碰撞,这是Hertz接触的非光滑(非Lipschitz连续)扩展,它说明了粘弹性阻尼。我们使用修正方程的技术来构造非耗散赫兹定律的时间离散,该耗散赫兹定律将数值耗散与KK耗散在不同的一致性阶次下进行匹配。这使我们能够以较高的精度模拟耗散冲击,而不会在接触力中包括非光滑的KK粘弹性分量。此定制的数值耗散是在牛顿动力学系统的通用框架中开发的,该系统要承受与保守力的时间导数成比例的耗散力。进行了数值测试,以模拟牛顿摇篮中的冲击以及交替的大小球的对准。所产生的波现象(振荡器同步,耗散孤波的传播,振荡尾部)可以通过具有定制的数值耗散的隐式方案精确捕获,即使是相对较大的时间步长也是如此。
更新日期:2020-03-20
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