We consider a coupled model of free-flow and porous medium flow, governed by stationary Stokes and Darcy flow, respectively. The coupling between the two systems is enforced by introducing a single variable representing the normal flux across the interface. The problem is reduced to a system concerning only the interface flux variable, which is shown to be well-posed in appropriately weighted norms. An iterative solution scheme is then proposed to solve the reduced problem such that mass is conserved at each iteration. By introducing a preconditioner based on the weighted norms from the analysis, the performance of the iterative scheme is shown to be robust with respect to material and discretization parameters. By construction, the scheme is applicable to a wide range of locally conservative discretization schemes and we consider explicit examples in the framework of Mixed Finite Element methods. Finally, the theoretical results are confirmed with the use of numerical experiments.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2020035
Mots-clés : Coupled porous media and fluid flow, Mixed Finite Element method, mortar method, robust preconditioner
@article{M2AN_2020__54_6_2045_0,
author = {Boon, Wietse M.},
title = {A parameter-robust iterative method for {Stokes{\textendash}Darcy} problems retaining local mass conservation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2045--2067},
publisher = {EDP-Sciences},
volume = {54},
number = {6},
year = {2020},
doi = {10.1051/m2an/2020035},
mrnumber = {4160325},
zbl = {1486.65279},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2020035/}
}
TY - JOUR AU - Boon, Wietse M. TI - A parameter-robust iterative method for Stokes–Darcy problems retaining local mass conservation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2020 SP - 2045 EP - 2067 VL - 54 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2020035/ DO - 10.1051/m2an/2020035 LA - en ID - M2AN_2020__54_6_2045_0 ER -
%0 Journal Article %A Boon, Wietse M. %T A parameter-robust iterative method for Stokes–Darcy problems retaining local mass conservation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2020 %P 2045-2067 %V 54 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2020035/ %R 10.1051/m2an/2020035 %G en %F M2AN_2020__54_6_2045_0
Boon, Wietse M. A parameter-robust iterative method for Stokes–Darcy problems retaining local mass conservation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 6, pp. 2045-2067. doi : 10.1051/m2an/2020035. http://www.numdam.org/articles/10.1051/m2an/2020035/
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