An ensemble domain decomposition method based on the stochastic collocation method for the random Stokes–Darcy models

We investigate a numerical method for the uncertainty quantification of Stokes–Darcy models with random hydraulic conductivity tensors and random source terms. The proposed method combines two independent strategies: an ensemble domain decomposition method, which enables the efficient computation of an ensemble of deterministic Stokes–Darcy problems, and a sparse-grid stochastic collocation method, which provides an accurate discretization of the probability space. To illustrate the performance of the method, we present three numerical examples. The results demonstrate that the method is capable of effectively capturing the impact of randomness in the coupled flow system while significantly reducing the computational cost.