Um Problema de Escoamento Bifásico em Meio Poroso com Função de Fluxo Descontínua

Abstract

In this work we study a nonlinear partial equation of the conservation law type that models a two-phase ow in a porous medium. The model considers the e ect of gravity on the ow, as well as the mediums heterogeneity, which features a discontinuity on the ux function. At the beginning we consider the Riemann problem, which consists in determining the solutions of the di erential equation subject to constant piecewise initial conditions. By using proper entropy conditions, we determine the sequences of rarefaction waves and shock waves that build the solution of this initial value problem, which yields an additional stationary shock because of the mediums heterogeneity.