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

多孔介质流动与自由流动的耦合问题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，这是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，研究人员将研究一个新的耦合多物理多尺度模型来描述两相耦合，相应的解耦数值方法来有效和准确地解决这个模型，以及两个数据同化方法来改善模型预测。这项工作的应用包括岩溶水系统，碳封存，石油开采，地热系统在裂缝性水库，地表和地下流动之间的相互作用，以及工业过滤。该项目为学生提供数据建模，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的广泛合作经验。该项目也是计算和应用数学计划和密苏里州计算和应用数学科学研究所在密苏里州ST的扩展的一部分，有可能使整个工程为基础的大学受益，并帮助密苏里州加强其在计算数学研究。在克莱姆森的研究人员将继续高中外展活动。耦合两个组成模型导致一个复杂的系统，涉及不同尺度的两相多孔介质流动和两相流体流动，这需要准确和有效的数值方法。由于数据量大和数据同化方法的迭代性质，使用现有数据来改进模式预测进一步增加了复杂性和计算成本。非线性、时间依赖性、真实界面/边界条件和数据信息在动态系统中的相互作用增加了模型的复杂性和计算规模，导致这种复杂的多物理场多尺度模型在耦合两相多孔介质流动和两相流体流动方面面临重大挑战。本项目将采用新提出的具有变密度和粘度的Cahn-Hilliard-Navier-Stokes-Darcy模型，在实验室数据支持的相场建模、稳定解耦方法、数据同化以及耦合多孔介质中两相流和两相自由流的数学分析方面开展新的研究。这项研究动态地将所有这些组成部分结合到一个混合的研究和开发系统中，该系统将利用新颖的数学建模/方法/分析与验证/数据同化/应用中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了基础。该奖项反映了NSF的法定使命，并被认为值得通过评估来支持使用基金会的知识价值和更广泛的影响审查标准。

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.