An Efficient Model for Flows of Large Number of Particles at Moderate to High Reynolds Numbers and Its Applications

这个建议开发了一个计算模型，用于模拟在不同的雷诺数（Re）的流体中的许多相互作用的粒子。该模型在计算效率和精度上都是新颖的。它吸收了欧拉和拉格朗日方法的跨学科知识和优势。它使用一个固定的网格来解决流场的光谱精度，并跟踪拉格朗日参考中的所有粒子。它避免了（1）精细网格来解决颗粒的边界层，（2）重复重新网格化的颗粒移动，3）多重网格，和（4）对流体场的许多刚性约束。该模型继承了以前的球绕流粒子分辨模型和谱元方法的精度，能够捕获中高Re下的粒子阻力，精度接近直接数值模拟。由于每个粒子只需要一个核函数，该模型模拟了大量粒子的流动，只需要一小部分额外的时间来求解流体相，并且比直接数值模拟快一到两个数量级。该模型提供了一个可行的方法来研究颗粒流涉及这么多的颗粒，其他颗粒解决方法可能是繁琐的。将在广泛的Re范围内对100，000至1，000，000个沉积物颗粒进行大规模模拟，以推断对海岸现场应用和海岸侵蚀有重要意义的宏观尺度参数。超过53%的美国人口居住在沿海地区，这些地区拥有丰富的自然和经济资源。在过去的世纪里，由于海平面上升、强风暴以及河流和海岸普遍的人为改变的共同影响，海岸地区正在经历快速的侵蚀。减轻海岸侵蚀需要提高模拟河流、河口和近海沉积物动力学的能力，以应对自然过程和人类活动共同造成的损害。除了海岸工程和环境工程外，流体与大量浸没颗粒的共轭相互作用在机械工程、化学工程、燃烧和石油加工等领域都具有重要意义。该模型为科学和工程的许多领域提供了先进的模拟工具，特别是有助于预测泥沙输运，减轻海岸侵蚀，改善环境管理。这一多学科研究的知识将用于培养研究生。该项目的成功将加速我们在计算颗粒流体流动方面的知识，并有助于更好地了解海岸侵蚀的机制。这项研究的发现将有助于防止海岸侵蚀，保护沿海居民和基础设施。

This proposal develops a computational model for simulating numerous interactive particles in a fluid at various Reynolds numbers (Re). This model is novel in the computational efficiency and accuracy. It assimilates interdisciplinary knowledge and strengths of Eulerian and Lagrangian approaches. It uses one fixed mesh to resolve the fluid field with spectral accuracy and to track all particles in a Lagrangian reference. It avoids (1) fine mesh to resolve the boundary layers of particles, (2) repetitive re-meshing as particles move, 3) multi-gridding, and (4) many stiff constraints on the fluid field. Inherited the accuracy from its previous particle-resolving model for flow around spheres and spectral element methods, this model is capable of capturing drag forces of particles at moderate to high Re with the accuracy close to a direct numerical simulation. Since only one kernel function per particle is needed, this model simulates a flow of large numbers of particles with only a small extra percentage of the time for solving only the fluid phase and is one to two orders faster than a direct numerical simulation. This model provides a viable method for studying particulate flows involving so many particles that other particle-resolving methods could be cumbersome. Large-scale simulation of 100,000 to 1,000,000 sediment grains will be conducted in a wide range of Re to infer macro-scale parameters significant to coastal field application and coastal erosion.More than 53% of the U.S. population lives in coastal regions, which are home to a wealth of natural and economic resources. Due to collective impacts of sea level rise, severe storms, and pervasive anthropogenic alterations of rivers and the coast over the past century, coastal regions are undergoing fast erosion. Mitigating coastal erosion requires improved capability of modeling sediment dynamics in rivers, estuaries and coastal seas in response to the detriment due to combined natural processes and anthropogenic activities. In addition to coastal and environmental engineering, the conjugate interactions of a fluid and large numbers of immersed particles are of vital significance to mechanical engineering, chemical engineering, combustion and petroleum processing etc. The proposed model provides an advanced simulation tool for many areas in science and engineering, and especially contributes to predicting sediment transport, mitigating coastal erosion, and improving environmental management. Knowledge in this multidisciplinary research will be used to train graduate students. The success of this project will accelerate our knowledge in computational particulate fluid flows and help better understand the mechanisms of coastal erosion. The discovery of this research will help prevent coastal erosion and protect the coastal inhabitants and infrastructure.