TY - JOUR
T1 - A Parallel Domain Decomposition Method for the Fully-Mixed Stokes-Dual-Permeability Fluid Flow Model with Beavers-Joseph Interface Conditions
AU - Li , Zheng
AU - Shi , Feng
AU - Sun , Yizhong
AU - Zhang , Yuhong
AU - Zheng , Haibiao
JO - Communications in Computational Physics
VL - 2
SP - 551
EP - 580
PY - 2024
DA - 2024/09
SN - 36
DO - http://doi.org/10.4208/cicp.OA-2023-0258
UR - https://global-sci.org/intro/article_detail/cicp/23392.html
KW - Stokes-dual-permeability model, Beavers-Joseph interface conditions, Robin-type domain decomposition, parallel computation, optimized Robin parameters.
AB - <p style="text-align: justify;">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 microfracture
flow 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 Sobolev
spaces. Based on the completely decoupled modified weak formulation, the mesh-independent geometric convergence rate of the proposed iterative parallel algorithm
is proved rigorously with some suitable parameters. To carry out the convergence
analysis of our proposed algorithm, we utilize an important but general convergence
lemma for the steady-state problems. Finding the optimized Robin parameters that
can accelerate the convergence of the proposed algorithm is an open problem mentioned inhere. Finally, several numerical experiments are presented to illustrate and
validate the exclusive features of our proposed algorithm.</p>