Two-phase flows involving capillary barriers in heterogeneous porous media
Analysis of PDEs
2010-07-26 v1
Abstract
We consider a simplified model of a two-phase flow through a heterogeneous porous medium, in which the convection is neglected. This leads to a nonlinear degenerate parabolic problem in a domain shared in an arbitrary finite number of homogeneous porous media. We introduce a new way to connect capillary pressures on the interfaces between the homogeneous domains, which leads to a general notion of solution. We then compare this notion of solution with an existing one, showing that it allows to deal with a larger class of problems. We prove the existence of such a solution in a general case, then we prove the existence and the uniqueness of a regular solution in the one-dimensional case for regular enough initial data.
Keywords
Cite
@article{arxiv.1005.5634,
title = {Two-phase flows involving capillary barriers in heterogeneous porous media},
author = {Clément Cancès and Thierry Gallouet and Alessio Porretta},
journal= {arXiv preprint arXiv:1005.5634},
year = {2010}
}