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Improving estimates of critical time-steps for discrete element simulations

改进离散元仿真的关键时间步长的估计

基本信息

批准号：
EP/N004477/1
负责人：
Kevin John Hanley
金额：
$ 10.68万
依托单位：
University of Edinburgh
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2015
资助国家：
英国
起止时间：
2015 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FN004477%2F1
关键词：
Improving estimates critical time steps

项目摘要

Granular materials are almost ubiquitous in our daily lives and include soil particles, pharmaceuticals in solid dosage forms, tea, coffee and powdered food ingredients, e.g., flour, bran, salt, sugar or condensed milk. Researchers investigating granular materials often use computer simulations to study their behaviour in detail. One such software tool, discrete element modelling (DEM), has become extremely popular in the last 20 years due to its power and flexibility and its popularity continues to grow year-on-year. DEM is based on a time-stepping algorithm: some calculations are performed, then time is incremented by a tiny time-step before the calculations are repeated. The size of this time-step determines how quickly the simulation may be run; it is therefore advantageous to choose the largest possible time-step. However, there is a limiting value - the 'critical' time-step - beyond which the simulation becomes unstable and the results become invalid. Unfortunately, the methods used to estimate the critical time-step at present are crude and different approaches can lead to greatly differing estimates. The lack of an accurate method to estimate critical time-steps for non-trivial simulations means that large factors of safety are required. This is why small and unnecessarily conservative time-steps are often adopted which causes simulations to run slowly.The overall aim of this project is to improve upon existing approaches for estimating critical time-steps for DEM simulations. This overarching aim can be divided into four objectives. Firstly, bounds will be calculated on the critical time-step for the simplest possible DEM simulation with only two idealised particles. Once this objective has been fully met, objectives two and three involve extending this analysis to systems of many particles and including complications in the basic discrete element model. These objectives will be achieved using a well-established approach for analysing the stability of nonlinear dynamical systems. The final objective is to critically evaluate the current methods for estimating critical time-steps by comparison with the findings of this study.This study has many potential benefits. Being able to estimate critical time-steps more accurately will allow the factors of safety applied to simulation time-step to be reduced. This has potentially huge implications for efficiency: simulation durations could be reduced from days to several hours. It will also become feasible to run larger, more ambitious simulations than was formerly the case. For example, a researcher who is barely able to run a simulation containing 100,000 particles might be able to increase the number of particles five-fold, without a commensurate increase in the duration of their simulation, by simply choosing a less conservative time-step. As the results of this study will be published openly and disseminated widely, this research will also be useful for increasing the efficiency of other related multi-body simulation codes. Furthermore, there are obvious environmental benefits as DEM simulations at all scales may be run in less time if the time-step can be increased without compromising the stability of the simulation.

颗粒材料在我们的日常生活中几乎无处不在，包括土壤颗粒、固体剂型的药物、茶、咖啡和粉状食品成分，例如，面粉、麸皮、盐、糖或炼乳。研究颗粒材料的研究人员经常使用计算机模拟来详细研究它们的行为。其中一种软件工具，离散元建模（DEM），由于其强大的功能和灵活性，在过去20年中变得非常受欢迎，并且其受欢迎程度逐年增长。DEM基于时间步进算法：执行一些计算，然后在重复计算之前将时间增加一个微小的时间步长。这个时间步长的大小决定了模拟运行的速度;因此，选择最大的时间步长是有利的。然而，有一个极限值-“临界”时间步长-超过该值，模拟变得不稳定，结果变得无效。不幸的是，目前用于估计关键时间步骤的方法是粗略的，不同的方法可能导致非常不同的估计。缺乏一个准确的方法来估计关键的时间步长的非平凡的模拟意味着大的安全系数是必需的。这就是为什么经常采用小的和不必要的保守的时间步长，导致模拟运行缓慢。本项目的总体目标是改善现有的方法，估计DEM模拟的关键时间步长。这一总体目标可分为四个目标。首先，边界将计算的临界时间步长为最简单的可能DEM模拟只有两个理想化的粒子。一旦这个目标已经完全满足，目标二和三涉及扩展这种分析的许多粒子的系统，包括复杂的基本离散元模型。这些目标将使用一个行之有效的方法来分析非线性动力系统的稳定性。最后的目的是批判性地评估目前的方法估计关键时间步的比较与本研究的结果。能够更准确地估计临界时间步长将允许应用于模拟时间步长的安全系数减小。这对效率有着潜在的巨大影响：模拟持续时间可以从几天减少到几个小时。与以前相比，运行更大、更雄心勃勃的模拟也将变得可行。例如，一个几乎无法运行包含100，000个粒子的模拟的研究人员可以通过简单地选择一个不太保守的时间步长来将粒子数量增加五倍，而不会相应地增加模拟的持续时间。由于这项研究的结果将公开发表并广泛传播，这项研究也将有助于提高其他相关多体仿真代码的效率。此外，有明显的环境效益，DEM模拟在所有尺度可以在更短的时间内运行，如果时间步长可以增加，而不影响模拟的稳定性。