A Non-iterative, Domain Decomposition Method with Different Time Step Sizes for the Evolutionary Stokes-darcy Model

This report analyzes a partitioned time stepping algorithm, meaning a non-iterative, domain decomposition method, which allows different time steps in the fluid region and the porous region for the fully evolutionary Stokes-Darcy problem. The method presented requires only one, uncoupled Stokes and Darcy sub-physics and sub-domain solve per time step. Under a time step restriction of the form 4t ≤ C(physical parameters) we prove stability and convergence of the method. Numerical tests are given confirming the convergence theory and demonstrating the computational efficiency of the partitioned method. They also show that in (the expected case) of greater fluid velocities in the free-flow region than in the porous media region, allowing smaller timesteps in the subregion with the faster velocities increases both accuracy and efficiency.