A well-posed hysteresis model for flows in porous media and applications to fingering effects

Abstract

We investigate ow problems in unsaturated porous media with hysteresis effects in the capillary pressure relation. The model expands the Richards equation, gravity is included and the space dimension is arbitrary. The hysteresis model has been suggested by experimentalists, static hysteresis is incorporated with a play-type model and additional dynamic effects are included. We propose a Galerkin scheme for these equations, show the convergence of the corresponding approximate solutions and the existence of weak solutions to the original problem. We include numerical results that show the effect of gravity driven fingering in porous media.