A hydraulic fracturing system with super-hydrophobic proppants is characterized by a transient triple-porosity Navier-Stokes model. For this complex multiphysics system, particularly in the context of three-dimensional space, a local parallel and non-iterative finite element method based on two-grid discretizations is proposed. The underlying idea behind utilizing the local parallel approach is to combine a decoupled method, a two-grid method and a domain decomposition method. The strategy allows us to initially capture low-frequency data across the decoupled domain using a coarse grid. Then it tackles high-frequency components by solving residual equations within overlapping subdomains by employing finer grids and local parallel procedures at each time step. By utilizing this approach, a significant improvement in computational efficiency can be achieved. Furthermore, the convergence results of the approximate solutions from the algorithm are obtained. Finally, we perform 2D/3D numerical experiments to demonstrate the effectiveness and efficiency of the algorithm as well as to illustrate its advantages in application.

翻译：超疏水支撑剂的水力压裂系统由瞬态三重孔隙Navier-Stokes模型描述。针对这一复杂多物理场系统，尤其在三维空间背景下，本文提出了一种基于两重网格离散的局部并行非迭代有限元方法。利用局部并行方法的核心思想在于将解耦方法、两重网格方法与区域分解方法相结合。该策略首先通过粗网格捕获解耦域中的低频数据，随后在每个时间步利用更细网格和局部并行程序求解重叠子域内的残差方程，从而处理高频分量。采用该方法可显著提升计算效率。此外，本文获得了算法近似解的收敛性结果。最后，通过2D/3D数值实验验证了该算法的有效性和效率，并展示了其应用优势。