Python Framework for HP Adaptive Discontinuous Galerkin Method for Two Phase Flow in Porous Media
For researchers in computational porous media flow, this provides a flexible, open-source implementation of hp-adaptive DG methods, though it is an incremental contribution building on existing Dune infrastructure.
The paper presents a Python framework for solving two-phase flow in porous media using an hp-adaptive Discontinuous Galerkin method, implemented via Dune-FemPy. It demonstrates flexible time-stepping and adaptation strategies, with code available as Jupyter notebooks.
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.