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Collaborative Research: Data-enabled Modeling, Numerical Method, and Data Assimilation for Coupling Dual Porosity Flow with Free Flow

协作研究：双孔隙流动与自由流动耦合的数据建模、数值方法和数据同化

基本信息

批准号：
1722692
负责人：
Craig Douglas
金额：
$ 15万
依托单位：
University of Wyoming
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-08-01 至 2021-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1722692&HistoricalAwards=false
关键词：
Collaborative Research Data enabled Modeling

项目摘要

The coupling of dual porosity flow and free flow arises in many important applications. However, the existing Stokes-Darcy types of models cannot accurately describe this type of coupled problem since they only consider single porosity media. Therefore, with the support of lab experiment data, the PIs develop a new coupled multi-physics multi-scale model and the corresponding numerical methods for accurately describing this coupling. Furthermore, both the lab and field datum provide the possibility to improve the accuracy of the model prediction through data assimilation. This project provides students many valuable training opportunities in data-enabled modeling, development of numerical methods and code packages, data assimilation, mathematical analysis, and engineering applications. They can gain solid foundation in computational math and data science, valuable research experience, and extensive collaboration experience with engineers. Starting from this collaboration work, the investigators plan to disseminate the proposed model, methods, and packages to more engineers and scientists for solving their realistic problems, present the work in professional conferences and colloquia, and organize special sessions in conferences for related works. Moreover, this project is part of the expansion of the computational and applied mathematics program and Missouri Institute for Computational and Applied Mathematical Sciences at Missouri S&T. This department-oriented expansion will benefit the entire engineering-based university and help state of Missouri enhance its relatively less active research in computational mathematics. At the University of Wyoming, the mathematics and statistics departments are merging in 2017 with a new emphasis on data sciences, mathematics, and statistics. This project will provide an immediate boost to the data science initiative and provide a justification for recruiting new students, scientists, and faculty.It is challenging to propose appropriate interface conditions for the new model in order to couple the two flows in a physically valid way. Moreover, coupling two constituent models leads to a complex system involving different scales in the dual porosity flow and the free flow, which demands accurate and efficient numerical methods. The use of existing data to improve the model prediction will even further increase the complexity and computational cost by a significant amount due to the big amount of data and iterative feature of the data assimilation methods. When the nonlinearity, time-dependence, realistic interface/boundary conditions, and data information interact with each other in a dynamic system, the whole system becomes much more complicated and much larger in computational scale. Therefore, significant challenges still remain for the intricate multi-physics multi-scale model to couple the dual porosity flow with the free flow. This project proposes a dual-porosity-Navier-Stokes model with the support of lab experiment data, develops the decoupled non-iterative multi-physics domain decomposition method with optimal convergence rates, study the variational data assimilation method with a newly defined cost function for improving the interface model prediction, carries out the mathematical analysis for the model and the numerical methods, and applies them to one or two applications. This research dynamically combines all of these components into a hybrid system of research and development that will take full advantage of the inherent relationship between the novel mathematical modeling/methods/analysis and the practical engineering advances in validation/data assimilation/applications, hence will lay the groundwork for reliable modeling of many applications involving complex flow in fractured porous media with highly-conductive conduits.

双重孔隙流动和自由流动的耦合在许多重要的应用中出现。然而，现有的Stokes-Darcy模型由于只考虑单一孔隙介质，无法准确描述这类耦合问题。因此，在实验室实验数据的支持下，pi开发了一种新的多物理场多尺度耦合模型和相应的数值方法来准确描述这种耦合。此外，实验室和现场数据都提供了通过数据同化来提高模型预测精度的可能性。该项目为学生提供了许多有价值的训练机会，包括数据建模、数值方法和代码包的开发、数据同化、数学分析和工程应用。他们可以在计算数学和数据科学方面获得坚实的基础，宝贵的研究经验，以及与工程师的广泛合作经验。从这项合作工作开始，研究人员计划将提出的模型、方法和包传播给更多的工程师和科学家，以解决他们的实际问题，在专业会议和学术会议上展示工作，并在会议上组织专题会议进行相关工作。此外，该项目是密苏里大学计算与应用数学计划和密苏里大学计算与应用数学科学研究所扩展的一部分。这种以院系为导向的扩展将使整个以工程为基础的大学受益，并帮助密苏里州加强其相对不太活跃的计算数学研究。在怀俄明大学，数学和统计部门将于2017年合并，新的重点是数据科学、数学和统计。该项目将立即推动数据科学计划，并为招募新学生、科学家和教师提供理由。为新模型提出合适的接口条件，以便以物理有效的方式耦合两个流是一项挑战。此外，两组分模型的耦合导致双重孔隙流动和自由流动的复杂系统涉及不同尺度，这需要精确和高效的数值方法。利用已有的数据来改进模型预测，由于数据同化方法的数据量大，且具有迭代的特点，会进一步增加模型预测的复杂度和计算成本。当非线性、时变、现实界面/边界条件和数据信息在动态系统中相互作用时，整个系统变得更加复杂，计算规模也更大。因此，复杂的多物理场多尺度模型将双重孔隙流动与自由流动耦合起来仍然是一个重大挑战。本课题在实验室实验数据的支持下，提出了双孔隙度- navier - stokes模型，开发了具有最优收敛速率的解耦非迭代多物理场域分解方法，研究了新定义代价函数的变分数据同化方法，以改进界面模型预测，并对模型和数值方法进行了数学分析，并将其应用于一到两个应用。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，该系统将充分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，因此将为涉及高导电性裂缝多孔介质中复杂流动的许多应用的可靠建模奠定基础。