R. Hilfer and R. Steinle
Institute for Computational Physics, Universität Stuttgart, 70569 Stuttgart, Germany
Abstract.
Saturation overshoot and hysteresis for two phase flow
in porous media are briefly reviewed. Old and new
challenges are discussed.
It is widely accepted that the traditional Richards model for
twophase flow in porous media does not support non-monotone
travelling wave solutions for the saturation profile.
As a concequence various extensions and generalizations
have been recently discussed.
The review highlights different limits
within the traditional theory. It emphasizes the relevance of
hysteresis in the Buckley-Leverett limit with jump-type hysteresis
in the relative permeabilities.
Reviewing the situation it emerges that the traditional
theory may have been abandoned prematurely because of
its inability to predict saturation overshoot in
the Richards limit.
