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

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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.