Abstract
We describe the competitive motion of incompressible immiscible phases within a porous medium as the gradient flow of a singular energy in the space of nonnegative measures with prescribed masses, endowed with some tensorial Wasserstein distance. We show the convergence of the approximation obtained by a minimization scheme á la R. Jordan, D. Kinderlehrer and F. Otto (SIAM J. Math. Anal. 29:1 (1998) 1–17). This allows us to obtain a new existence result for a physically well-established system of PDEs consisting of the Darcy–Muskat law for each phase, 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.
Citation
Clément Cancès. Thomas O. Gallouët. Léonard Monsaingeon. "Incompressible immiscible multiphase flows in porous media: a variational approach." Anal. PDE 10 (8) 1845 - 1876, 2017. https://doi.org/10.2140/apde.2017.10.1845
Information