SAV Decoupled Ensemble Algorithm for the Dual‐Porosity‐Stokes Model With Uncertainty Quantification

We present an ensemble algorithm for the dual‐porosity‐Stokes model with random intrinsic permeabilities in the matrix and microfracture. This model arises in various applications such as hydrology, industrial filtration, and petroleum extraction. Our algorithm combines a scalar auxiliary variable (SAV) approach, an ensemble idea, and a decoupled strategy to achieve high accuracy and efficiency. The SAV approach removes the stability restriction on the time‐step size. The ensemble idea reduces the storage and time cost of constructing coefficient matrices for different samples with random parameters. The decoupled strategy splits the dual‐porosity‐Stokes model into three simple systems (five sub‐problems) that can be solved independently by using the IMEX method. We prove that our algorithm is unconditionally long‐time stable and optimally convergent. We also demonstrate its performance and applications through three numerical experiments, especially a 3D model problem for the horizontal open‐hole completion wellbore.