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A Global-in-time Domain Decomposition Method for the Coupled Nonlinear Stokes and Darcy Flows

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Abstract

We study a decoupling iterative algorithm based on domain decomposition for the time-dependent nonlinear Stokes–Darcy model, in which different time steps can be used in the flow region and in the porous medium. The coupled system is formulated as a space-time interface problem based on the interface condition for mass conservation. The nonlinear interface problem is then solved by a nested iteration approach which involves, at each Newton iteration, the solution of a linearized interface problem and, at each Krylov iteration, parallel solution of time-dependent linearized Stokes and Darcy problems. Consequently, local discretizations in time (and in space) can be used to efficiently handle multiphysics systems of coupled equations evolving at different temporal scales. Numerical results with nonconforming time grids are presented to illustrate the performance of the proposed method.

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  1. Department of Mathematics and Statistics, Auburn University, Auburn, AL, 36849, USA

    Thi-Thao-Phuong Hoang

  2. School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC, 29634, USA

    Hyesuk Lee

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T.-T.-P. Hoang’s work is partially supported by the US National Science Foundation under grant number DMS-1912626 and Auburn University’s intramural grants program.

H. Lee’s work is partially supported by the US National Science Foundation under grant number DMS-1818842.

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Hoang, TTP., Lee, H. A Global-in-time Domain Decomposition Method for the Coupled Nonlinear Stokes and Darcy Flows. J Sci Comput 87, 22 (2021). https://doi.org/10.1007/s10915-021-01422-1

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