A Local and Parallel FEMs Based on the 2D/3D Nonstationary Stochastic Dual‐Porosity Navier–Stokes Model

ABSTRACT This article proposes an effective local parallel algorithm for the rapid resolution of the stochastic dual‐porosity Navier–Stokes model. The Monte Carlo method addresses random input coupling models, while a series of deterministic models are computed using a local parallel algorithm. The algorithm allows three decoupled subproblems to be solved in parallel using a coarse grid to obtain the low‐frequency component. Then, a finer grid is used to solve the residual equation in the overlapping subdomain, thereby obtaining the high‐frequency component. This approach significantly enhances computational efficiency. The convergence of the numerical solution is rigorously established. A series of numerical experiments validates the effectiveness and efficiency of the proposed method.