Non-Iterative Multi-Physics Domain Decomposition Method for the Navier-Stokes-Darcy Model

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The Navier-Stokes-Darcy model is crucial to accurately describe many important real world problems, such as the flow problems in vuggy/fractured porous media, groundwater systems in karst aquifers, interaction between surface and subsurface flows, and industrial filtrations. The efficiency of the numerical methods to solve this model is very important for the large-scale applications. But most of the related published works focus on a simpler model, which is not accurate for many applications since it does not consider several crucial realistic factors. This project is to study a more realistic Navier-Stokes-Darcy model and design an efficient numerical method to solve it in parallel. The completion of this project will provide large advances in the study of the coupled fluid flow and porous media flow. The basic idea and framework of this project have potential to be applied to other interesting multi-physics coupling problems. This project provides undergraduate and graduate students many valuable training opportunities in the development of new methods and packages, mathematical analysis, and engineering applications. The methods under development will be applied to simulate the flow in vuggy/fractured porous media. The investigators plan to disseminate the methods and software packages to more engineers and scientists by presenting the work in professional conferences and colloquia and organizing special sessions. The goal of this project is to carry out a systematic research on the development, analysis, and application of a non-iterative multi-physics domain decomposition method for the Navier-Stokes-Darcy model with the Beavers-Joseph (BJ) interface condition and defective boundary conditions. The proposed non-iterative multi-physics domain decomposition method enables us to efficiently and simultaneously deal with the significant difficulties arising from the interaction among the aforementioned crucial realistic factors. The key ideas include a non-iterative algorithm with a direct prediction on the interface, a multi-physics decomposition with Robin conditions arising from the three physical interface conditions which include the BJ condition, and the Lagrange multiplier method to deal with the defective boundary condition. The major difficulty is the inherent interaction of the nonlinear advection, BJ condition, parameters in the Robin-Robin decomposition, and the saddle point problem arising from the Lagrange multiplier method.