A Parallel Domain Decomposition Method for the Fully-Mixed Stokes-Dual-Permeability Fluid Flow Model with Beavers-Joseph Interface Conditions (Communications in Computational Physics, 2024)
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 weakformulation are constructed to completely decouple the original problem, not only forthe free flow and dual-permeability regions but also for the matrix and microfractureflow fields 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 Sobolevspaces. Based on the completely decoupled modified weak formulation, the mesh-independent geometric convergence rate of the proposed iterative parallel algorithmis proved rigorously with some suitable parameters. To carry out the convergenceanalysis of our proposed algorithm, we utilize an important but general convergencelemma for the steady-state problems. Finding the optimized Robin parameters thatcan accelerate the convergence of the proposed algorithm is an open problem mentioned inhere. Finally, several numerical experiments are presented to illustrate andvalidate the exclusive features of our proposed algorithm.