Continuum modelling of particulate flows in nature and industry

自然界和人造世界的大部分都是由离散的固体颗粒组成的。然而，目前还没有完全令人满意的理论来描述它们在工业和地球物理学中重要的许多复杂流动场景中的运动。尽管面临诸多挑战，但在过去的20年里，一个充满希望的范例已经建立起来。基于关键的实验、数学和物理见解，干燥颗粒流动和悬浮在背景流体中的颗粒流动的连续体模型开始成熟。在这个项目中，驱动目标将是开发一种统一的流变学，跨越颗粒材料可以表现出的许多流动状态。一旦这个模型开始形成，新的数值方法将被开发来求解结果动力学方程。然后，该内部代码将应用于各种测试用例，这些测试用例受到自然流动的启发，例如碎屑雪崩和海底滑坡，以及工业中，例如漏斗流动和鼓式搅拌机。这项工作将被一些关键的开放性问题所框架和激励，如“将颗粒流动动力学分为类气体、类液体和类固体行为在建模中有用吗？”，“解决多态颗粒流动方程的最合适的数值方法是什么？”以及“液态水的存在如何改变自然灾害的严重程度和工业过程的效率？”。

So much of the natural and man-made world is composed of collections of discrete solid grains. However, there is currently no completely satisfactory theory to describe their motion, en masse, in the many complex flow scenarios which are important across industry and geophysics. Despite the challenges, a promising paradigm has been building over the last 20 years. Based around key experimental, mathematical and physical insights, continuum models for both the flow of dry grains and for particles suspended in a background fluid are beginning to mature.In this project, the driving goal will be to develop a unified rheology spanning the many flow regimes that particulate materials can exhibit. Once this model begins to take shape, novel numerical methods will be developed to solve the resultant dynamical equations. This in-house code will then be applied to various test cases inspired by flows in nature, such as debris avalanches and subsea landslides, and in industry, such as hopper flows and drum mixers.The work will be framed and motivated by key open questions such as "Is it useful in modelling to categorise particle flow dynamics into gas-like, liquid-like and solid-like behaviour?", "What is the most appropriate numerical method to solve multi-regime particulate flow equations?" and "How does the presence of liquid water modify the severity of natural hazards and the efficiency of industrial processes?".