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

Dedner, Andreas ; Kane, Birane ; Klöfkorn, Robert LU orcid and Nolte, Martin (2019) In Applied Mathematical Modelling 67. p.179-200
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.

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author
; ; and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Discontinuous Galerkin, Dune, hp-adaptivity, IMPES, Porous media two-phase flow, Python
in
Applied Mathematical Modelling
volume
67
pages
22 pages
publisher
Elsevier
external identifiers
  • scopus:85055911690
ISSN
0307-904X
DOI
10.1016/j.apm.2018.10.013
language
English
LU publication?
no
id
2d599438-2e7f-49e5-a9e1-559d841fda5f
date added to LUP
2021-02-10 14:02:16
date last changed
2022-04-27 00:11:50
@article{2d599438-2e7f-49e5-a9e1-559d841fda5f,
  abstract     = {{<p>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.</p>}},
  author       = {{Dedner, Andreas and Kane, Birane and Klöfkorn, Robert and Nolte, Martin}},
  issn         = {{0307-904X}},
  keywords     = {{Discontinuous Galerkin; Dune; hp-adaptivity; IMPES; Porous media two-phase flow; Python}},
  language     = {{eng}},
  pages        = {{179--200}},
  publisher    = {{Elsevier}},
  series       = {{Applied Mathematical Modelling}},
  title        = {{Python framework for hp-adaptive discontinuous Galerkin methods for two-phase flow in porous media}},
  url          = {{http://dx.doi.org/10.1016/j.apm.2018.10.013}},
  doi          = {{10.1016/j.apm.2018.10.013}},
  volume       = {{67}},
  year         = {{2019}},
}