Advisor: Florin Radu
Short description of the project:
In this thesis, we compare different iterative approaches for solving the non-linear, coupled multiphase flow and reactive transport in porous media. Especially, we consider two-phase flow and one a-half phase flow (modeled by Richards equation) coupled with a one-component transport equation. Implicit and explicit iterative schemes will be compared in terms of efficiency, robustness, and accuracy. The best approach seems to be a fully implicit scheme, which is a slightly modified variant of the classical splitting iterative scheme for coupled equations. We concentrate on three linearization methods: L-scheme, Modified Picard and Newton. We implement them in Matlab and tested them on both an academic example, built from a manufactured analytical solution and on a realistic problem, the Salinity Problem. In the first part of the thesis, we will also briefly study the generic two-phase flow plus transport equation in porous media, presenting some of the most common solving algorithms such as the IMPES method and its Fully Implicit reformulation.