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Averaging of flows with capillary hysteresis in stochastic porous media

Published online by Cambridge University Press:  01 June 2007

BEN SCHWEIZER
BEN SCHWEIZER*
Affiliation:
Mathematisches Institut, Universität Basel, Rheinsprung 21, CH-4051 Basel, Switzerland email: [email protected]
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Abstract

Fluids in unsaturated porous media are described by the relationship between pressure (p) and saturation (u). Darcy's law and conservation of mass provides an evolution equation for u, and the capillary pressure provides a relation between p and u of the form p∈ pc(u,∂tu). The multi-valued function pc leads to hysteresis effects. We construct weak and strong solutions to the hysteresis system and homogenize the system for oscillatory stochastic coefficients. The effective equations contain a new dependent variable that encodes the history of the wetting process and provide a better description of the physical system.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 18 , Issue 3 , June 2007 , pp. 389 - 415
Copyright
Copyright © Cambridge University Press 2007

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