# A Multi-grid Decoupling Method for the Coupled Fluid Flow with the Porous Media Flow

A Multi-grid Decoupling Method for the Coupled Fluid Flow with the Porous Media Flow 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Mathematical Fluid Mechanics Springer Journals

# A Multi-grid Decoupling Method for the Coupled Fluid Flow with the Porous Media Flow

Journal of Mathematical Fluid Mechanics, Volume 20 (2) – Sep 22, 2017
13 pages

/lp/springer_journal/a-multi-grid-decoupling-method-for-the-coupled-fluid-flow-with-the-G5k8IHVYEZ
Publisher
Springer Journals
Subject
Physics; Fluid- and Aerodynamics; Mathematical Methods in Physics; Classical and Continuum Physics
ISSN
1422-6928
eISSN
1422-6952
D.O.I.
10.1007/s00021-017-0340-7
Publisher site
See Article on Publisher Site

### Abstract

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

Journal of Mathematical Fluid MechanicsSpringer Journals

Published: Sep 22, 2017

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