A high order ensemble algorithm for dual-porosity-Navier-Stokes flows

Abstract

In this paper, we introduce and analyze an efficient high-order ensemble algorithm incorporating the semi-implicit spectral deferred correction (SDC-Ensemble algorithm) tailored to simulate flows exhibiting multiple realizations within the stochastic dual-porosity-Navier-Stokes system. This framework accommodates uncertainties stemming from initial conditions, forcing terms, interface boundary conditions and the hydraulic conductivity tensor. By consolidating all realizations into a unified coefficient matrix at each time step, the SDC-Ensemble algorithm significantly diminishes computational overhead compared to traditional methods that treat each realization independently, while preserving high-order accuracy. Furthermore, it disentangles the dual-porosity-Navier-Stokes system into three manageable sub-physics problems, thereby reducing the dimensionality of linear systems and facilitating parallel computation. Employing some novel techniques, this paper also provides a comprehensive stability analysis for the proposed method without relying on the theoretical stability results of lower-order ensemble algorithms. Numerical experiments corroborate the theoretical findings and illustrate the applicability of the algorithm and its features to flow problems in multistage fractured horizontal wellbore with appropriate boundary/interface conditions.