Incompressible immiscible multiphase flows in porous media: a variational approach
Analysis of PDEs
2018-03-16 v2 Optimization and Control
Abstract
We describe the competitive motion of (N + 1) incompressible immiscible phases within a porous medium as the gradient flow of a singular energy in the space of non-negative measures with prescribed mass endowed with some tensorial Wasserstein distance. We show the convergence of the approximation obtained by a minimization schem\`e a la [R. Jordan, D. Kinder-lehrer \& F. Otto, SIAM J. Math. Anal, 29(1):1--17, 1998]. This allow to obtain a new existence result for a physically well-established system of PDEs consisting in the Darcy-Muskat law for each phase, N capillary pressure relations, and a constraint on the volume occupied by the fluid. Our study does not require the introduction of any global or complementary pressure.
Keywords
Cite
@article{arxiv.1607.04009,
title = {Incompressible immiscible multiphase flows in porous media: a variational approach},
author = {Clément Cancès and Thomas Gallouët and Leonard Monsaingeon},
journal= {arXiv preprint arXiv:1607.04009},
year = {2018}
}