Modeling and simulation of non-monotonic waves in two-phase flows

Abstract

The main objective of this research is to provide a thorough understanding of the non- monotonic behaviors of solutions to the two-phase flow equations in porous media. To achieve this objective, numerical modeling and simulation have been performed. Specific objectives are as follows. 1. Simulate the saturation overshoot phenomenon observed in laboratory experiments and study the effects of different models with and without hysteretic effects. 2. Numerically investigate the relationship between the overshoot saturation and the dynamic capillary coefficient, the infiltrating flux rate, the initial and boundary values, and resolve the steep wave fronts by using an adaptive moving mesh method. 3. Study the non-monotonic solutions of the non-equilibrium Richards equation and the modified Buckley-Leverett equation by applying a moving mesh method and choosing different flux reconstruction schemes. 4. Design an accurate discontinuous Galerkin method for the modified Buckley-Leverett equation and study the influences of order and limiting strategy. 5. Because of the inspiration of the thin film flow, Cueto-Felgueroso and Juanes [47] proposed a phase field model for the two-phase porous media flow. Hence, we will investigate the thin film flow equation and resolve the non-monotonic structures using an adaptive moving mesh finite element method.