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

这一建议开发了一个计算模型，用于模拟流体中具有不同雷诺数(Re)的大量相互作用的粒子。该模型在计算效率和计算精度上具有一定的新颖性。它吸收了欧拉和拉格朗日方法的跨学科知识和长处。它使用一个固定的网格，以光谱精度求解流场，并跟踪拉格朗日参考中的所有粒子。它避免了(1)用于解决粒子边界层的精细网格，(2)粒子移动时的重复重新网格划分，(3)多重网格，以及(4)对流场的许多刚性约束。该模型继承了以往球体绕流粒子分辨模型和谱单元方法的精度，能够捕捉中高Re粒子的阻力，精度接近直接数值模拟。由于每个粒子只需要一个核函数，因此该模型模拟了大量粒子的流动，只需要很小的额外百分比的时间来仅求解流体相，并且比直接数值模拟快一到两个数量级。该模型为研究涉及如此多颗粒的颗粒流提供了一种可行的方法，以至于其他颗粒解析方法可能很麻烦。将在大范围内对10万至100万个沉积物颗粒进行大规模模拟，以推断对海岸野外应用和海岸侵蚀具有重要意义的宏观尺度参数。美国53%以上的人口生活在沿海地区，那里拥有丰富的自然和经济资源。在过去的一个世纪里，由于海平面上升、强风暴以及普遍存在的河流和海岸的人为改变的集体影响，沿海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、河口和沿海海域沉积物动力学的能力，以应对自然过程和人为活动综合造成的损害。除了海岸工程和环境工程外，流体和大量浸没颗粒的共轭相互作用对于机械工程、化工、燃烧和石油加工等领域都具有重要意义。该模型为许多科学和工程领域提供了先进的模拟工具，特别是在预测泥沙运动、减轻海岸侵蚀和改善环境管理方面做出了贡献。这项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.