Non-overlapping domain decomposition for Stokes-Darcy couplings

Ivan Yotov

Email: yotov@math.pitt.edu
Postal address: Department of Mathematics, 301 Thackeray Hall, University of Pittsburgh, Pittsburgh, PA 15260

We discuss a mathematical and numerical model for coupling Stokes and Darcy flows through the Beavers-Joseph-Saffman interface conditions. The discrete formulation couples conforming Stokes elements with mixed finite elements and utilizes a Lagrange multiplier to impose the interface conditions. An-overlapping domain decomposition algorithm is developed which reduces the coupled algebraic system to an interface problem. The number of interface variables changes with the type of the interface. In particular, normal stress is used on Stokes-Darcy and Darcy-Darcy interfaces, while both normal stress and tangential stress are used on Stokes-Stokes interfaces. Each interface iteration requires solving Stokes or Darcy subdomain problems.  It is shown that the interface problem is symmetric and positive definite and that its condition number is $O(1/h)$, where $h$ is the discretization parameter. Numerical results and parallel scalability studies are presented.