Partitioned Time Stepping Method for Fully Evolutionary Navier-Stokes/Darcy Flow with BJS Interface Conditions

Abstract

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 ${\bf u}\cdot {\bf n}_f>0$ (not hold for general case but still in many situation, such as the gentle river). Under a modest time step restriction of the form $\Delta  t\leq C$, 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.