Affiliations: Equipe d'Analyse Numérique, Université de Saint-Etienne, 23 rue du Docteur Paul Michelon, 42023 Saint-Etienne Cedex France | Ruder Boskovic Institute, PO Box 1016, 41001 Zagreb, Croatia
Note: [] Correspondence to: A. Mikelić, Laboratoire d'Analyse Numérique, Bât. 101, Université Lyon 1, 43, Bd. du onze novembre 1918,69622 Villeurbanne Cedex, France.
Note: [] Permanent address after October 1,1992: Laboratoire d'Analyse Numérique, Bât. 101, Université Lyon 1, 43, Bd. du onze novembre 1918, 69622 Villeurbanne Cedex, France.
Abstract: We consider the hyperbolic-elliptic coupled nonlinear system describing two-phase immiscible flows, with neglected capillary pressure, through a one-dimensional porous medium. We prove the existence and uniqueness of an entropy solution for data corresponding to the solution with discontinuities in saturations. Then we study the homogenization of this system when the permeability and porosity are rapidly oscillating. We get the stability of our coupled system, due to the very special underlying structure of this system in one dimension. Finally we discuss the behavior of the system with oscillatory initial saturation. This result also contains the homogenization of two-component miscible flow in a one-dimensional porous medium, without any dispersion term, as a special case.
