In this paper, we propose a multi-grid decoupling method for the coupled Navier–Stokes–Darcy problem with the Beavers–Joseph–Saffman interface condition. The basic idea of the method is to first solve a much smaller global problem on a very coarse initial grid, then solve a linearized Newton problem and a Darcy problem in parallel on all the subsequently refined grids. Error bounds of the approximate solution for the proposed method are analyzed, and optimal error estimates are obtained. Numerical experiments are conducted to verify the theoretical analysis and indicate the effectiveness of the proposed method.
Journal of Mathematical Fluid Mechanics – Springer Journals
Published: Sep 22, 2017
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