Partitioned time stepping method for fully evolutionary Stokes-Darcy flow with Beavers-Joseph interface conditions

In this report, a partitioned time stepping algorithm for transient flow in a matrix domain coupled to a free flow in embedded conduits is analyzed. The coupled flow is modeled by the fully evolutionary Stokes-Darcy problem. This method requires solving only one, uncoupled Stokes and Darcy subphysics and subdomain per time step. On the interface between the matrix and conduit, Beavers-Joseph interface conditions, instead of the simplified Beavers-Joseph-Saffman condition, are imposed. Under a modest time step restriction of the form Δt ≤ C, where C = C (physical parameters) we prove stability of the method. We also derive error estimates. Numerical tests illustrate the validity of the theoretical results.