Python framework for hp-adaptive discontinuous Galerkin methods for two-phase flow in porous media

Abstract

• Presentation of a framework for solving two phase flow problems in porous media . • Easy to use python frontend and a state-of-the-art C++ backend based on well established software package DUNE. • hp-adaptive Discontinuous Galerkin Method for two phase flow in porous media. • Comparison of five different solution techniques from fully coupled fully implicit to loosely coupled splitting schemes. In this paper we present a framework for solving two-phase flow problems in porous media. The discretization is based on a Discontinuous Galerkin method and includes local grid adaptivity and local choice of polynomial degree. The method is implemented using the new Python frontend Dune-FemPy to the open source framework Dune. The code used for the simulations is made available as Jupyter notebook and can be used through a Docker container. We present a number of time stepping approaches ranging from a classical IMPES method to a fully coupled implicit scheme. The implementation of the discretization is very flexible allowing to test different formulations of the two-phase flow model and adaptation strategies.