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.

双孔隙流动和自由流动的耦合出现在许多重要的应用中。然而，现有的 Stokes-Darcy 类型的模型无法准确描述此类耦合问题，因为它们仅考虑单一孔隙介质。因此，在实验室实验数据的支持下，PI开发了一种新的耦合多物理场多尺度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提高模型预测准确性的可能性。该项目为学生提供了许多宝贵的培训机会，涉及数据建模、数值方法和代码包开发、数据同化、数学分析和工程应用。他们可以获得计算数学和数据科学方面的坚实基础、宝贵的研究经验以及与工程师的广泛合作经验。从这项合作工作开始，研究人员计划将所提出的模型、方法和包传播给更多的工程师和科学家，以解决他们的现实问题，在专业会议和学术讨论会上展示工作，并在相关工作的会议中组织特别会议。此外，该项目是密苏里科技大学计算和应用数学项目和密苏里州计算和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张将使整个工程大学受益，并帮助密苏里州加强其相对不太活跃的计算数学研究。怀俄明大学的数学系和统计系将于 2017 年合并，新的重点是数据科学、数学和统计学。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。为新模型提出适当的接口条件，以便以物理有效的方式耦合两个流是具有挑战性的。此外，耦合两个组成模型会导致一个复杂的系统，涉及不同尺度的双孔隙流动和自由流动，这需要准确有效的数值方法。由于数据同化方法的数据量大且具有迭代特性，利用现有数据来改进模型预测将进一步大幅增加复杂性和计算成本。当非线性、时间依赖性、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，计算规模也变得更大。因此，复杂的多物理场多尺度模型将双孔隙率流动与自由流动耦合仍然存在重大挑战。该项目在实验室实验数据的支持下提出了双孔隙纳维斯托克斯模型，开发了具有最佳收敛速度的解耦非迭代多物理域分解方法，研究了具有新定义的成本函数的变分数据同化方法改进界面模型预测，对模型和数值方法进行数学分析，并将其应用于一到两个应用中。这项研究将所有这些组件动态地组合成一个混合的研究和开发系统，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，从而奠定为涉及具有高导电性管道的裂隙多孔介质中的复杂流动的许多应用进行可靠建模奠定了基础。