An artificial compressibility ensemble algorithm for a stochastic Stokes-Darcy model with random hydraulic conductivity and interface conditions

We propose and analyze an efficient ensemble algorithm with artificial compressibility (AC) for fast decoupled computation of multiple realizations of the stochastic Stokes-Darcy model with random hydraulic conductivity (including the one in the interface conditions), source terms, and initial conditions. The solutions are found by solving three smaller decoupled subproblems with two common time-independent coefficient matrices for all realizations, which significantly improves the efficiency for both assembling and solving the matrix systems. The fully coupled Stokes-Darcy system can be first decoupled into two smaller subphysics problems by the idea of the partitioned time stepping, which reduces the size of the linear systems and allows parallel computing for each subphysics problem. The AC further decouples the velocity and pressure which further reduces storage requirements and improves computational efficiency. We prove the long time stability and the convergence for this new ensemble method. Three numerical examples are presented to support the theoretical results and illustrate the features of the algorithm, including the convergence, stability, efficiency, and applicability.