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Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2018

WELL-POSED STOKES/BRINKMAN AND STOKES/DARCY COUPLING REVISITED WITH NEW JUMP INTERFACE CONDITIONS

Philippe Angot

Résumé

The global well-posedness in time is proved, with no restriction on the size of the data, for the Stokes/Brinkman and Stokes/Darcy coupled flow problems with new jump interface conditions recently derived in [11] by asymptotic modelling and shown to be physically relevant. These original conditions include jumps of both stress and tangential velocity vectors at the fluid-porous interface. They can be viewed as generalizations for the multi-dimensional flow of Beavers & Joseph's jump condition of tangential velocity and Ochoa-Tapia & Whitaker's jump condition of shear stress. Therefore, they are different from those most commonly used in the literature. The case of Saffman's approximation is also studied, but with a force balance for the cross-flow including the Darcy drag and inducing a law of pressure jump different from the usual one. The proof of these results follows the general framework briefly introduced in [7, 8] for the steady flow.
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Dates et versions

hal-01635289 , version 1 (15-11-2017)

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Philippe Angot. WELL-POSED STOKES/BRINKMAN AND STOKES/DARCY COUPLING REVISITED WITH NEW JUMP INTERFACE CONDITIONS. ESAIM: Mathematical Modelling and Numerical Analysis, 2018, 52 (5), pp.1875--1911. ⟨10.1051/m2an/2017060⟩. ⟨hal-01635289⟩
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