Python Framework for HP Adaptive Discontinuous Galerkin Method for Two Phase Flow in Porous Media

TL;DR

This paper introduces a flexible Python-based framework utilizing Discontinuous Galerkin methods with adaptive meshing for simulating two-phase flow in porous media, supporting various time-stepping schemes.

Contribution

It presents a novel Python framework integrating local adaptivity and polynomial degree choice for two-phase flow modeling in porous media.

Findings

Framework supports multiple time-stepping methods including IMPES and fully coupled schemes.

Implementation is flexible, allowing testing of different flow formulations and adaptation strategies.

Code is accessible via Jupyter notebooks and Docker, facilitating reproducibility and ease of use.

Abstract

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 fully coupled implicit scheme. The implementation of the discretization is very flexible allowing for test different formulations of the two phase flow model and adaptation strategies.