Hysteresis models and gravity fingering in porous media

We study flow problems in unsaturated porous media. Our main interest is the gravity driven penetration of a dry material, a situation in which fingering effects can be observed experimentally and numerically. The flow is described by either a Richards or a two-phase model. The important modelling aspect regards the capillary pressure relation which can include static hysteresis and dynamic corrections. We report on analytical existence and instability results for the corresponding models and present numerical calculations. We show that fingering effects can be observed in various models and discuss the importance of the static hysteresis term