论文标题
平行结构域分解方法，用于与海狸约瑟夫界面条件的完全混合的dual-dual-exmeabebeality流动流量模型
Parallel Domain Decomposition method for the fully-mixed Stokes-dual-permeability fluid flow model with Beavers-Joseph interface conditions
论文作者
论文摘要
在本文中，提出了一种平行结构域分解方法，用于求解使用海狸 - 约瑟夫（BJ）界面条件的完全混合的dual-exmeabeabeality流动流量模型。构建了三个罗宾型边界条件和修改的弱配方，以完全解散原始问题，这不仅是针对自由流和双渗透性区域的，而且对于双孔隙率介质中的矩阵和微裂纹。我们得出了具有适当兼容条件的原始问题与解耦系统之间的等价性，并且还证明了不同Sobolev空间中两个弱公式的等效性。基于完全脱钩的修饰弱公式，严格证明了迭代平行算法的收敛性。为了对我们提出的算法进行收敛分析，我们为稳态问题提出了一个重要但一般的收敛引理。此外，有了一些合适的参数选择，新算法被证明可以达到几何收敛速率。最后，提出了一些数值实验，以说明和验证我们提出的算法的性能和独家特征。
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.
