Numerical model of gravity segregation of two-phase fluid in porous media based on hybrid upwinding

Abstract

Abstract The paper discusses the numerical algorithm constructing a three-dimensional model for a flow of two-phase incompressible fluid caused by the mass force of gravity in a porous medium. The algorithm is based on a combination of a hybrid upwind method with an explicit scheme for determination of the saturation. The hybrid upwinding allows us to take into account flows of fluid of various nature (in this case, viscous and gravitational flows) separately, which is extremely important in the case of gravitational flow with opposite directions of phase flows. The explicit scheme being extremely simple in implementation provides a small dispersion of solutions on discontinuities. The proposed algorithm is illustrated by the results of numerical experiments demonstrating the monotonicity of the method considered in this paper.