RUI: Computational Models for Coupled Free/Porous Media Flow

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This project will study fluid flow models with applications in human health and the environment. The focus is on models that combine a free fluid part and a porous media part. For example, in physiology, such fluid flow models help to understand transport of oxygen and nutrients between blood vessels and tissue. In hydrology, such models can be used to study and predict contamination by toxic chemicals from leaky underground storage tanks or landfills mixing with groundwater. In industrial filtration, the flow models studied in this project can be incorporated into more complex models to optimize the design of the three-way catalytic converter used to reduce vehicle emission levels. Efficient computer simulation of these coupled free/porous flows remains challenging due to the multi-physics nature of the systems. This research aims to develop accurate and efficient numerical simulation techniques for such models. The project provides training through undergraduate research experiences.This project studies models of coupled flow systems using the incompressible Stokes equations in the free domain and the Darcy equations in the porous domain. An advection-diffusion equation is added to the system to model the transport phenomena at the free/porous interface. The research aims to develop, analyze, and implement an integrated numerical model of this system of equations in three dimensions. The main goals are to (i) address severe limitations of the direct solution, due to incompatibilities in the differential operators in the free and porous subdomains, (ii) develop robust, high accuracy, and well-conditioned integral equation formulations, (iii) apply rigorous analysis on the iterative methods to deduce optimal convergence, and (iv) add the ability to combine different methods of discretization to effectively model heterogeneous porous media. The project will develop a new boundary integral formulation, with regularization and correction for high accuracy, and a simple quadrature based on implicit representation of the surface. Efficient domain decomposition methods with new transmission conditions based on non-local operators will be used to speed up the iteration process. High-performance computing techniques and a kernel-independent treecode algorithm will be implemented to increase the speed of computations.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.