4.7 Article

Domain decomposition method for the fully-mixed Stokes-Darcy coupled problem

出版社

ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2020.113578

关键词

Stokes-Darcy coupled problem; Robin-type domain decomposition; Parallel computation

资金

  1. NSF of China [11971174]
  2. NSF of Shanghai, PR China [19ZR1414300]
  3. National Natural Science Foundation of China [12071040]
  4. Zhujiang Scholar program, PR China
  5. Science and Technology Commission of Shanghai Municipality, PR China [18dz2271000, 19JC1420102]
  6. United International College (BNU-HKBU) [R72021111]

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In this paper, a parallel domain decomposition method is proposed for solving the fully-mixed Stokes-Darcy coupled problem with the Beavers-Joseph-Saffman interface conditions. The method decouples the original problem into two independent subproblems with newly constructed Robin-type boundary conditions and modified weak formulation. Convergence analysis and numerical examples demonstrate the effectiveness of the proposed method.
In this paper, a parallel domain decomposition method is proposed, for solving the fully-mixed Stokes-Darcy coupled problem with the Beavers-Joseph-Saffman (BJS) interface conditions. With newly constructed Robin-type boundary conditions, the present method adopts modified weak formulation to decouple the original problem into two independent subproblems. The equivalence between the original problem and the decoupled subproblems is derived under some compatibility conditions. Another equivalence of two weak formulations with different spaces is also established, for subsequent convergence analysis based on the decoupled modified weak formulation. Moreover, the convergence of the iterative parallel method in a more general framework is shown. With some suitable choice of parameters, both mesh-dependent and mesh-independent convergence rates are proved rigorously. Finally, we present several numerical examples to show the exclusive features of the proposed method. (C) 2020 Elsevier B.V. All rights reserved.

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