Dimensional reduction by Fourier analysis of a Stokes-Darcy fracture model - Laboratoire Jean-Alexandre Dieudonné Accéder directement au contenu
Proceedings/Recueil Des Communications Année : 2023

Dimensional reduction by Fourier analysis of a Stokes-Darcy fracture model

Martin J Gander
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Julian Hennicker
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Roland Masson
Tommaso Vanzan
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Résumé

We consider a Stokes flow along a thin fracture coupled to a Darcy flow in the surrounding matrix domain. In order to derive a dimensionally reduced model representing the fracture as an interface coupled to the surrounding matrix, we extend the methodology based on Fourier analysis developed in [1] for a Darcy-Darcy coupling. We show that this approach not only allows us to derive error estimates between the solutions of the full and mixed-dimensional models, but also leads to a model correction term compared with what is obtained from the classical reduction technique based on integration along the fracture width combined with profile closure assumptions [3, 2].
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Dates et versions

hal-04105535 , version 1 (24-05-2023)

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Martin J Gander, Julian Hennicker, Roland Masson, Tommaso Vanzan. Dimensional reduction by Fourier analysis of a Stokes-Darcy fracture model. 432, Springer Nature Switzerland, pp.295-304, 2023, Springer Proceedings in Mathematics & Statistics, ⟨10.1007/978-3-031-40864-9_24⟩. ⟨hal-04105535⟩
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