Collaborative Research: Laboratory Data Enabled Phase Field Modeling and Data Assimilation for Coupled Two-Phase Fluid Flow and Porous Media Flow

多孔介质流动和自由流动的耦合在许多重要的应用中出现。然而，大多数文献只考虑单相模型，这并不适用于涉及两相流的地球物理应用。在实验室实验数据的支持下，研究了描述两相耦合的新型多物理场多尺度耦合模型，高效、准确求解该模型的解耦数值方法，以及改进模型预测的两种数据同化方法。本研究的应用领域包括岩溶含水层的地下水系统、固碳、石油开采、裂缝性储层的地热系统、地表和地下流动的相互作用以及工业过滤。该项目为学生提供了数据建模、数值方法和代码包开发、数据同化方法、数学分析和工程应用等方面的培训机会。参与该项目的学生可以获得计算数学和数据科学的坚实基础，宝贵的研究经验，以及与工程师广泛的合作经验。该项目也是密苏里理工大学计算与应用数学项目和密苏里计算与应用数学科学研究所扩展的一部分，该研究所有可能使整个工程大学受益，并帮助密苏里州加强其在计算数学方面的研究。克莱姆森大学的调查员将继续开展高中外展活动。两组分模型的耦合导致两相多孔介质流动和两相流体流动的复杂系统涉及不同的尺度，这需要精确和高效的数值方法。利用已有数据来改进模型预测，由于数据量大和数据同化方法的迭代性，进一步增加了模型预测的复杂性和计算成本。动态系统中非线性、时变、现实界面/边界条件和数据信息的相互作用增加了模型的复杂性和计算规模，给复杂的多物理场多尺度模型耦合两相多孔介质流和两相流体流带来了重大挑战。本项目将采用新提出的变密度和变粘度Cahn-Hilliard-Navier-Stokes-Darcy模型，对实验室数据支持的相场建模、稳定解耦方法、数据同化和耦合多孔介质中两相流与两相自由流的数学分析进行新颖的研究。本研究动态地将所有这些组成部分结合到一个混合研究和开发系统中，该系统将利用新颖的数学建模/方法/分析与验证/数据同化/应用方面的实际工程进展之间的内在关系，为许多相关应用的可靠建模奠定基础。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。

The coupling of porous media flow and free flow arises in many important applications. However, most literature considers only single-phase models, which are not applicable for geophysical applications involving two-phase flows. With the support of lab experiment data, the investigators will study a new coupled multi-physics multi-scale model for describing the two-phase coupling, the corresponding decoupling numerical methods for efficiently and accurately solving this model, and two data assimilation methods for improving the model prediction. Applications of this work include groundwater systems in karst aquafer, carbon sequestration, petroleum extraction, geothermal systems in fractured reservoirs, interaction between surface and subsurface flows, and industrial filtrations. This project provides students training opportunities in data-enabled modeling, development of numerical methods and code packages, data assimilation methods, mathematical analysis, and engineering applications. Students involved in this project can gain a solid foundation in computational math and data science, valuable research experience, and extensive collaboration experience with engineers. This project is also part of the expansion of the computational and applied mathematics program and Missouri Institute for Computational and Applied Mathematical Sciences at Missouri S&T which has the potential to benefit the entire engineering-based university and help the state of Missouri enhance its research in computational mathematics. The investigator at Clemson will continue high school outreach activities.Coupling two constituent models leads to a complex system involving different scales in the two-phase porous media flow and two-phase fluid flow, which demands accurate and efficient numerical methods. The use of existing data to improve the model prediction further increases the complexity and computational cost due to the large amount of data and the iterative nature of the data assimilation methods. The interaction of nonlinearity, time-dependence, realistic interface/boundary conditions, and data information in a dynamic system increases the model complexity and computational scale, leading to significant challenges for this intricate multi-physics multi-scale model in coupling the two-phase porous media flow and two-phase fluid flow. This project will carry out novel research on lab data enabled phase field modeling, stable decoupling method, data assimilation, and mathematical analysis for coupling two-phase flow in porous media with two-phase free flow, by using a newly proposed Cahn-Hilliard-Navier-Stokes-Darcy model with varying densities and viscosities. This research dynamically combines all of these components into a hybrid system of research and development that will take advantage of the inherent relationship between the novel mathematical modeling/methods/analysis and the practical engineering advances in validation/data assimilation/applications, laying the groundwork for reliable modeling of many relevant applications.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.