Fast and Accurate Artificial Compressibility Ensemble Algorithms for Computing Parameterized Stokes-Darcy Flow Ensembles

Accurate simulations of the Stokes-Darcy system face many difficulties including the coupling of flows in two different subdomains via interface conditions, the incompressibility constraint for the free flow and uncertainties in model parameters. In this report, we propose and study efficient, decoupled, artificial compressibility (AC) ensemble schemes based on a recently developed SAV approach for fast computation of Stokes-Darcy flow ensembles. The proposed algorithms (1) do not require any time step condition and (2) decouple the computation of the velocity and pressure in the free flow region, and (3) result in a common coefficient matrix for all realizations after spatial discretization for which efficient iterative linear solvers such as block CG or block GMRES can be used to greatly reduce the computational cost. We prove the long time stability under two parameter conditions, without any timestep constraints. In particular, for one single simulation, they are unconditionally stable schemes. Several numerical tests are presented to demonstrate the efficiency of the algorithms and illustrate their applications in realistic flow problems.