Second-Order Fast Ensemble Algorithm for Dual-Porosity-Stokes Model with Random Physical Parameters

In this paper, we propose and analyze a second-order fast ensemble algorithm for simulation of the dual-porosity-Stokes model with random intrinsic permeabilities. The strong heterogeneity of the physical parameters results in the huge associated uncertainties in the data, hence simulations for this type of problem require repeated sampling. In this case, the efficiency of the algorithms is a particularly important issue. Our proposed algorithm uses a BDF2-AB2 scheme for time discretization. By adopting the mean value of samples, the coefficient matrices are kept independent of the sampling procedure, which means that we only need to solve three groups of linear systems that share the same coefficient matrices, respectively for all realizations. As expected, it is much less expensive than the traditional decoupled approach without ensemble. Under a time-step condition and three physical parameter constrictions, we prove that our algorithm is long-time stable and optimal convergent theoretically. Moreover, three numerical experiments are implemented, the numerical results verify the feasibility and efficiency of our second-order fast ensemble algorithm.