The recently developed dual-porosity-Stokes model describes a complicated dual-porosity-conduit system which uses a dual-porosity/permeability model to govern the flow in porous media coupled with free flow via four physical interface conditions. This system has important applications in unconventional reservoirs especially the multistage fractured horizontal wellbore problems. In this paper, we propose and analyze domain decomposition methods to decouple the large system arisen from the discretization of dual-porosity-Stokes model. Robin boundary conditions are used to decouple the coupling conditions on the interface. Then, Robin-Robin domain decomposition methods are constructed based on the two decoupled sub-problems. Convergence analysis is demonstrated and a geometric convergence order is obtained. Optimized Schwarz methods are proposed for the dual-porosity-Stokes model and optimized Robin parameters are obtained to improve the convergence of proposed algorithms. Three computational experiments are presented to illustrate and validate the accuracy and applicability of proposed algorithms.

最近开发的双孔隙度-斯托克斯模型描述了一种复杂的双孔隙度-导管系统，该系统使用双孔隙度/渗透率模型来控制多孔介质中的流动以及通过四个物理接口条件的自由流动。该系统在非常规油藏特别是多级裂缝水平井眼问题中具有重要的应用。在本文中，我们提出并分析了域分解方法，以解耦由双孔隙度-斯托克斯模型离散化产生的大型系统。Robin边界条件用于解耦接口上的耦合条件。然后，基于两个解耦的子问题构造了Robin-Robin域分解方法。证明了收敛性分析并获得了几何收敛阶。针对双孔隙度Stokes模型提出了优化的Schwarz方法，并获得了优化的Robin参数以提高算法的收敛性。提出了三个计算实验来说明和验证所提出算法的准确性和适用性。