Coupled Flow and Transport Modeling and Simulation of Complex Fluids and Extreme Weather Patterns by Harnessing Data

复杂的流体和龙卷风可以通过研究流动和输送的耦合来从数学上理解。复杂流体被用于许多重要领域，包括医药、军事和石油工业，仅举几例。Shell小组最近的实验结果表明，在蠕虫状胶束流体中观察到的剪切诱导结构可以有效地用于提高采收率。拟议的研究将提供一个所需的定量理解虫状胶束流体。龙卷风是一种复杂的气象现象，通常与强对流大气条件有关。根据美国国家海洋和大气管理局/国家气象局的数据，2021年已经确认发生了超过797次龙卷风。由于全球变暖，龙卷风也变得越来越频繁和严重。提出的研究将阐明对龙卷风形成的理解，这对于制定适当的龙卷风预警问题至关重要，从而避免灾难性的破坏和人员伤亡。该项目将开发保守的、离散的、保持最大原则的、高效的数值格式，用于模拟在复杂流体和龙卷风等重要研究领域中出现的耦合流动和输送。这些新方法将进行数学分析，并通过使用一类新的快速求解器来大大降低计算瓶颈的复杂性。PI在这个项目中开发的框架将使研究人员能够解决几十年来计算流变学家难以捉摸的各种物理参数。兼容的窗口物理通知神经网络将尝试解决正则化复杂流体。该项目将提出一种新的龙卷风模型，用于理解蒸汽-颗粒反应、对流和扩散中的极端微天气模式。特别是，该项目将阐明和填补数学建模与龙卷风现象之间的空白，从而加深对龙卷风形成的认识。此外，还将设计一个数据驱动的深度神经网络，用于确定龙卷风模型中的未知物理参数。该奖项反映了美国国家科学基金会的法定使命，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。

Complex fluids and tornadoes can be understood mathematically by studying a coupled flow and transports. Complex fluids are used in many important areas, including medicine, the military, and the oil industry, to name a few. Recent experimental results by Shell groups show that the shear induced structure observed in the wormlike micellar fluids can be effectively used for enhanced oil recovery. The proposed research will provide a desired quantitative understanding of wormlike micellar fluids. Tornadoes are complex meteorological phenomena that are often associated with severe convective atmospheric conditions. According to NOAA/National Weather Service, more than 797 tornadoes occurrences have already been confirmed in 2021. Tornadoes are becoming more frequent and severe due to global warming as well. The proposed research will elucidate the understanding of tornadogenesis, which is crucial to make a proper tornado warning issue, thereby avoiding catastrophic damage and casualties. This project will develop conservative, discrete maximum principle preserving, and efficient numerical schemes that can be used for simulating coupled flow and transports that arise in important areas of research, such as complex fluids and tornadoes. These new methods will be analyzed mathematically and enhanced by using a class of new fast solvers to drastically reduce the complexity of computational bottlenecks. The framework developed by the PI in this project will enable researchers to tackle a wide spectrum of physical parameters that have been elusive for computational rheologists for decades. Compatible window-wise physics informed neural network will be attempted to solve regularized complex fluids. The project will present a new tornado model for the understanding of extreme micro-weather patterns in vapor-to-particle reaction, convection, and diffusion. In particular, this project will elucidate and fill the gap between mathematical modeling and phenomena of tornadoes, thereby deepening the understanding of tornadogenesis. A data-driven deep neural networks will be designed for determining the unknown physical parameters in the tornado model as well.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.