In this paper, a parallel domain decomposition method is proposed for solving the fully-mixed Stokes-dual-permeability fluid flow model with Beavers-Joseph (BJ) interface conditions. Three Robin-type boundary conditions and a modified weak formulation are constructed to completely decouple the original problem, not only for the free flow and dual-permeability regions but also for the matrix and microfractures in the dual-porosity media. We derive the equivalence between the original problem and the decoupled systems with some suitable compatibility conditions, and also demonstrate the equivalence of two weak formulations in different Sobolev spaces. Based on the completely decoupled modified weak formulation, the convergence of the iterative parallel algorithm is proved rigorously. To carry out the convergence analysis of our proposed algorithm, we propose an important but general convergence lemma for the steady-state problems. Furthermore, with some suitable choice of parameters, the new algorithm is proved to achieve the geometric convergence rate. Finally, several numerical experiments are presented to illustrate and validate the performance and exclusive features of our proposed algorithm.
翻译:在本文中,提出了一种平行的域分解方法,用Beavers-Joseph(BJ)接口条件解决完全混合的斯托克斯双渗透流体流体模型,构建了三种Robin型边界条件和经修改的弱配方,以完全分解最初的问题,不仅针对自由流动和双渗透区域,而且针对双渗透介质中的矩阵和微裂变。我们从原始问题和分解的系统之间得出等值,并具备一些适当的兼容性条件,还展示了不同索博列夫空间两种微弱配方的等值。根据完全分解的变弱配方,迭接并行算法的趋同证明是严格的。为了对我们拟议的算法进行趋同分析,我们建议对稳定状态问题进行重要但普遍的混合列母体。此外,如果选择一些适当的参数,新的算法就证明可以达到几何趋同率。最后,提出了几项数字实验,以说明和验证我们提议的算法的性及排他性。