Selecting a suitable time step for discrete element simulations that use the central difference time integration scheme
Selecting a suitable time step for discrete element simulations that use the central difference time integration scheme
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DOI：
10.1108/02644400410519794
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发表时间：
2004-03
影响因子：
1.6
通讯作者：
C. O’Sullivan;J. Bray
中科院分区：
文献类型：
--
作者：
C. O’Sullivan;J. Bray
由Cundall和Strack提出的离散元法采用计算效率高、显式、中心差分时间积分格式。该方案的一个限制是它只能是条件稳定的，因此必须使用小的时间步长。一些研究人员提出使用隐式时间积分方案来避免在这些模拟中通常使用的显式时间积分所产生的稳定性问题。然而，这些方案的计算成本很高，并且可能需要大量的迭代来形成与每个时间步长结束时接触状态兼容的刚度矩阵。本文提出了一种新的、简单的计算显式离散元模拟中临界时间增量的方法。利用这种方法，证明了临界时间增量是当前接触条件的函数。考虑到二维和三维场景，提出的关键时间步长的改进估计表明，文献中包含的早期建议可能是不保守的，因为它们经常高估实际的关键时间步长。一个具有已知解析解的问题的三维模拟说明，如果时间增量超过稳定分析的临界时间步长，则从离散单元模拟中获得错误结果的可能性。
The distinct element method as proposed by Cundall and Strack uses the computationally efficient, explicit, central difference time integration scheme. A limitation of this scheme is that it is only conditionally stable, so small time steps must be used. Some researchers have proposed using an implicit time integration scheme to avoid the stability issues arising from the explicit time integrator typically used in these simulations. However, these schemes are computationally expensive and can require a significant number of iterations to form the stiffness matrix that is compatible with the contact state at the end of each time step. In this paper, a new, simple approach for calculating the critical time increment in explicit discrete element simulations is proposed. Using this approach, it is shown that the critical time increment is a function of the current contact conditions. Considering both two‐ and three‐dimensional scenarios, the proposed refined estimates of the critical time step indicate that the earlier recommendations contained in the literature can be unconservative, in that they often overestimate the actual critical time step. A three‐dimensional simulation of a problem with a known analytical solution illustrates the potential for erroneous results to be obtained from discrete element simulations, if the time‐increment exceeds the critical time step for stable analysis.