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

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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.