In this paper, two-grid finite element method for the steady dual-permeability-Stokes fluid flow model is proposed and analyzed. Dual-permeability-Stokes interface system has vast applications in many areas such as hydrocarbon recovery process, especially in hydraulically fractured tight/shale oil/gas reservoirs. Two-grid method is popular and convenient to solve a large multiphysics interface system by decoupling the coupled problem into several subproblems. Herein, the two-grid approach is used to reduce the coding task substantially, which provides computational flexibility without losing the approximate accuracy. Firstly, we solve a global problem through standard P_k − P_k− 1 − P_k − P_k finite elements on the coarse grid. After that, a coarse grid solution is applied for the decoupling between the interface terms and the mass exchange terms to solve three independent subproblems on the fine grid. The three independent parallel subproblems are the Stokes equations, the microfracture equations, and the matrix equations, respectively. Four numerical tests are presented to validate the numerical methods and illustrate the features of the dual-permeability-Stokes model.

提出并分析了稳态双渗透Stokes流体流动模型的两网格有限元方法。双渗透-斯托克斯接口系统在许多领域都具有广泛的应用，例如碳氢化合物的回收过程，尤其是在水力压裂的致密/页岩油/气储层中。通过将耦合问题分解成几个子问题，两网格方法很流行，而且很方便解决大型的多物理场接口系统。在本文中，两网格方法用于实质上减少编码任务，这提供了计算灵活性，而不会损失近似精度。首先，我们通过标准P _k - P _{k -1} - P _k - P解决全局问题粗网格上的_k个有限元。之后，将粗糙网格解决方案应用于界面项和质量交换项之间的解耦，以解决精细网格上的三个独立子问题。三个独立的并行子问题分别是斯托克斯方程，微断裂方程和矩阵方程。提出了四个数值测试来验证数值方法并说明双重渗透性-斯托克斯模型的特征。