Mesh filtration problems with a two-flow structure of phase velocities

Abstract

Abstract This paper deals with the problem of filtration of a two-phase incompressible fluid within the Buckley-Leverett model. From a general point of view, a two-flow structure of conservation laws is investigated. In addition, since the solution in the Buckley-Leverett model is discontinuous, conservation laws are presented in the generalized integral form. A good illustration of the approach presented is the problem of gravitational segregation of oil and water in a porous medium. For this problem, a two-flow mesh structure of conservation laws is described.