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.