Partitioned time stepping method with different time scales for a dual-porosity-Stokes model

Shan, Li; Zhang, Haicheng

doi:10.1016/j.apnum.2021.09.009

Cited by 5 publications

(1 citation statement)

References 27 publications

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“…Multi-domain, multi-physics coupled problems are significant in many natural and industrial applications, such as the groundwater fluid flow in the karst aquifer, petroleum extraction, industrial filtration, blood flow motion in the arteries, and so on. Up to now, a great deal of mathematical and physical models for free flow coupled with complicated porous media were constructed, including the Stokes-Darcy model [1][2][3][4], dual-porosity-Stokes model [5][6][7][8][9][10][11], etc. Typically, we usually utilize the Darcy equation in the traditional Stokes-Darcy fluid flow system to simulate the single porosity model.…”

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confidence: 99%

Parallel Domain Decomposition method for the fully-mixed Stokes-dual-permeability fluid flow model with Beavers-Joseph interface conditions

Li¹,

Shi²,

Sun³

et al. 2022

Preprint

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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.

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