(untitled) (Advances in Applied Mathematics and Mechanics, 2019)
In this report, a partitioned time stepping algorithm for Navier Stokes/Darcy model is analyzed. This method requires only solving one, uncoupled Navier Stokes and Darcy problems in two different sub-domains respectively per time step. On the interface, the simplified Beavers-Joseph-Saffman conditions are imposed with an additional assumption u· n_f>0 (not hold for general case but still in many situation, such as the gentle river). Under a modest time step restriction of the form Δ t≤ C, where C=C (physical parameters), we prove stability of the method and get the error estimates. Numerical tests illustrate the validity of the theoretical results.