A well-posed hysteresis model for flows in porous media and applications to fingering effects
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Date
2010-11-19
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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.