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

摘要

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