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

Andreas Dedner, Birane Kane, Robert Klöfkorn, Martin Nolte

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish
Pages (from-to)179-200
Number of pages22
JournalApplied Mathematical Modelling
Volume67
DOIs
Publication statusPublished - 2019 Mar
Externally publishedYes

Subject classification (UKÄ)

  • Computational Mathematics

Free keywords

  • Discontinuous Galerkin
  • Dune
  • hp-adaptivity
  • IMPES
  • Porous media two-phase flow
  • Python

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