Hysteresis in porous media: Modelling and analysis

Abstract

Unsaturated flow through porous media can be modelled by a partial differential equation using saturation $s$ and pressure $p$ as unknowns. Experimental data as well as elementary physical arguments show that the coupling of the two variables must take into account hysteresis. In this survey, we describe the physical origins of porous media hysteresis, present the ideas of its mathematical description, and review the analysis of the resulting hysteresis models.