Erosion, Transport, and Dispersion in Granular and Porous Media

天然存在的多孔和颗粒状材料，如土壤，沙子和粘土，通过过滤污染物和长期供应淡水，在调节地球水资源方面发挥着关键作用。对这种污染和过滤循环的理解依赖于多孔介质中的传输和分散现象，随着时间的推移，不断流动的地下水可以改变多孔介质本身的细节，例如单个沙粒的大小，形状和位置，这增加了复杂性。这些影响在快速事件中最为明显，例如天坑的重力塌陷，但也可能由于较慢过程的积累而发生，例如机械或化学侵蚀。该项目将利用先进的计算方法，详细研究地下水流改变多孔介质性质的快速和缓慢过程之间的相互作用。通过更深入地了解潜在的物理过程，该项目提供了更好地管理水资源的社会效益，面对外部因素，如污染或天坑形成。例如，本文中所形成的理解可以使得能够识别最易受污染或塌陷影响的特定区域。研究生将参与并接受该项目的指导和跨学科培训。该项目旨在通过使用大量新开发的计算工具和简化的数学模型来分析地球物理多孔介质应用中出现的一系列复杂的动力学问题。感兴趣的具体问题包括：（1）多孔介质的微观成分的侵蚀导致各向异性的宏观性质;（2）示踪剂通过介质的改变的运输，包括异常分散;和（3）灾难性事件的发生，如陷孔坍塌，由地下水渗流，侵蚀和浮力之间的相互作用造成的。该项目将解决几个计算的挑战和机遇。首先，规模的范围是巨大的：空间尺度从微观颗粒成分到大型地质含水层;时间尺度从突然的天坑坍塌到需要数年的机械和化学侵蚀。该系统本质上是多组分的，流体和固相之间存在耦合。虽然控制偏微分方程是线性的，但移动边界的存在会在几何形状和流动之间引入非线性反馈。计算流体动力学中的一个挑战是获得动态物体的稠密悬浮体的高保真模拟。利用积分方程法结合精确求积、快速求和法、接触算法和高阶时间步进，本项目将使用快速数值方法精确模拟各向异性侵蚀、溶解和沉积体的稠密悬浮液。混合规模的深度神经网络将用于从高保真数值模拟生成的数据中学习，以基于多相框架对粗粒度模型进行参数化。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Naturally occurring porous and granular materials, such as soil, sand, and clay, play a pivotal role in regulating the Earth's water resources by filtering contaminants and, over long timescales, supplying fresh water. Understanding of this contamination and filtration cycle relies on the phenomenon of transport and dispersion in porous media, with the added complexity that continually flowing groundwater can, over time, alter the details of the porous medium itself such as the size, shape, and position of individual sand grains. These effects are most noticeable during rapid events such as the gravitational collapse of a sinkhole, but can also occur due to the accumulation of slower processes, such as mechanical or chemical erosion. This project will leverage advanced computational methods to study in detail the interplay between fast and slow processes by which groundwater flow alters porous medium properties. By gaining a deeper understanding of the underlying physical processes, the project offers the societal benefit of better management of water resources in the face external factors, such as contamination or sinkhole formation. For example, the understanding developed herein may enable identification of specific regions most susceptible to contamination or to collapse. Graduate students will be involved and receive mentoring and interdisciplinary training in this project. This project is to analyze a set of complex, dynamical problems that arise in geophysical porous-media applications by using a host of newly developed computational tools and reduced mathematical models. The particular problems of interest include: (1) the erosion of microscopic constituents of porous media leading to anisotropic macroscopic properties; (2) the modified transport of tracers through the medium, including anomalous dispersion; and (3) the occurrence of catastrophic events, such as sink hole collapse, resulting from interaction between groundwater seepage, erosion, and buoyancy forces. The project will address several computational challenges and opportunities. First the range of scales is vast: spatial scales range from microscopic granular constituents to large geological aquifers; timescales range from that of a sudden sinkhole collapse to years required mechanical and chemical erosion. The systems are inherently multicomponent, with coupling between the fluid and solid phases. Although the governing PDEs are linear, the presence of moving boundaries introduces nonlinear feedback between geometry and flow. One challenge in computational fluid dynamics is to obtain high-fidelity simulations of dense suspensions of dynamic bodies. Using integral equation methods in conjunction with accurate quadrature, fast summation methods, contact algorithms, and high-order time stepping, this project will use fast numerical methods to accurately simulate dense suspensions of anisotropic eroding, dissolving, and sedimenting bodies. Mixed-scale, deep neural networks will be used to learn from the data generated by high-fidelity numerical simulations to parameterize coarse-grained models based on the multiphase framework.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.