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Advanced Numerical Methods in the Mathematical Sciences

ChangQing Wang, University of Pittsburgh
Domain Decomposition Method on Stokes-Darcy Flow


Coupling Stokes and Darcy equations is useful in many different applications, such as interaction of surface water and groundwater in aquifer, or interaction of blood flow through arterial walls, where Stokes equation describes the motion of incompressible fluids and Darcy equation describes the infiltration process. The equations are coupled through Beavers-Joseph-Saffman conditions on the interface between the Stokes and Darcy regions. Here we introduce a non-overlapping domain decomposition approach for the Stokes-Darcy coupled problem, where the computational domain is divided into subdomains for solving the problem in parallel. In this approach, we use finite element tearing and interconnect (FETI) method to deal with issues arising from floating Stokes subdomains and also a multiscale flux basis method to improve the computational efficiency.