Robin-Robin domain decomposition methods for the dual-porosity-conduit system. (English) Zbl 1467.76035
Summary: The recently developed dual-porosity-Stokes model describes a complicated dual-porosity-conduit system which uses a dual-porosity/permeability model to govern the flow in porous media coupled with free flow via four physical interface conditions. This system has important applications in unconventional reservoirs especially the multistage fractured horizontal wellbore problems. In this paper, we propose and analyze domain decomposition methods to decouple the large system arisen from the discretization of dual-porosity-Stokes model. Robin boundary conditions are used to decouple the coupling conditions on the interface. Then, Robin-Robin domain decomposition methods are constructed based on the two decoupled sub-problems. Convergence analysis is demonstrated and a geometric convergence order is obtained. Optimized Schwarz methods are proposed for the dual-porosity-Stokes model and optimized Robin parameters are obtained to improve the convergence of proposed algorithms. Three computational experiments are presented to illustrate and validate the accuracy and applicability of proposed algorithms.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76S05 | Flows in porous media; filtration; seepage |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
Keywords:
dual-porosity-Stokes flow model; finite element discretization; domain decomposition; optimized Schwarz method; multistage fractured wellboreReferences:
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