Vol. 4, No. 1, 2016

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ISSN: 2325-3444 (e-only)
ISSN: 2326-7186 (print)
Modeling capillary hysteresis in unsatured porous media

Gérard Gagneux and Olivier Millet

Vol. 4 (2016), No. 1, 67–77
Abstract

This paper deals with the modeling of cyclic hysteresis phenomena for flows in unsaturated porous media, using a dynamic regularization process of Sobolev type. The addition of a kinematic regularizing term of third-order partial derivatives, depending on a strictly positive, small real parameter, enables us to capture the missing information of the ill-posed hysteresis phenomena via Rankine–Hugoniot and “entropy” inequalities. When this parameter tends to zero, an oriented hysteresis loop, corresponding to the realistic problem modeled, emerges from the flow of an associated auxiliary ordinary differential equation.

Keywords
capillary hysteresis loop, unsaturated porous media
Mathematical Subject Classification 2010
Primary: 35K65
Secondary: 47J40, 76S05
Milestones
Received: 10 September 2015
Revised: 3 December 2015
Accepted: 15 January 2016
Published: 28 June 2016

Communicated by Francesco dell'Isola
Authors
Gérard Gagneux
Laboratoire des Sciences de l’Ingénieur pour l’Environnement, UMR-CNRS 7356
Université de La Rochelle
avenue Michel Crépeau
17042 La Rochelle Cedex 1
France
Olivier Millet
Laboratoire des Sciences de l’Ingénieur pour l’Environnement, UMR-CNRS 7356
Université de La Rochelle
avenue Michel Crépeau
17042 La Rochelle Cedex 1
France