Operator Splitting for Three-Phase Flow in Heterogeneous Porous Media (Communications in Computational Physics, 2009)
We describe an operator splitting technique based on physics rather thanon dimension for the numerical solution of a nonlinear system of partial differentialequations which models three-phase flow through heterogeneous porous media. Themodel for three-phase flow considered in this work takes into account capillary forces,general relations for the relative permeability functions and variable porosity and permeabilityfields. In our numerical procedure a high resolution, nonoscillatory, secondorder, conservative central difference scheme is used for the approximation of the nonlinearsystem of hyperbolic conservation laws modeling the convective transport of thefluid phases. This scheme is combined with locally conservative mixed finite elementsfor the numerical solution of the parabolic and elliptic problems associated with thediffusive transport of fluid phases and the pressure-velocity problem. This numericalprocedure has been used to investigate the existence and stability of nonclassical shockwaves (called transitional or undercompressive shock waves) in two-dimensional heterogeneousflows, thereby extending previous results for one-dimensional flow problems.Numerical experiments indicate that the operator splitting technique discussedhere leads to computational efficiency and accurate numerical results.