Stable across regimes : A mixed DG method for Darcy–Brinkman–Stokes type flows
Terschanski, Benjamin ; Klöfkorn, Robert LU
; Dedner, Andreas
and Kowalski, Julia
(2025)
In Computer Methods in Applied Mechanics and Engineering
442.
- Abstract
Hydromechanical models of Darcy–Brinkman–Stokes type consider mass- and momentum conservation of an incompressible fluid on a domain with varying permeability. They include the two important limits of free flow governed by the classical Navier–Stokes equations and porous Darcy flow. The conceptual simplicity makes the model attractive from a modeling perspective, but any numerical solution procedure is challenged by the description of flow domains with different stability requirements. Furthermore, spatial variations in the dominant physics, such as strongly localized rapid variations in permeability adversely affect the conditioning of resulting linear systems. In this publication, we propose a discretization based on mixed... (More)
Hydromechanical models of Darcy–Brinkman–Stokes type consider mass- and momentum conservation of an incompressible fluid on a domain with varying permeability. They include the two important limits of free flow governed by the classical Navier–Stokes equations and porous Darcy flow. The conceptual simplicity makes the model attractive from a modeling perspective, but any numerical solution procedure is challenged by the description of flow domains with different stability requirements. Furthermore, spatial variations in the dominant physics, such as strongly localized rapid variations in permeability adversely affect the conditioning of resulting linear systems. In this publication, we propose a discretization based on mixed discontinuous Galerkin Finite-Elements for the Darcy–Brinkman–Stokes model. The method leverages schemes proposed for the incompressible Navier–Stokes equations and for Darcy flow to obtain a robust solver in both flow limits, as well as for flows that sharply transition from high to low permeability regions. To this end, we introduce a mass-flux stabilization term. Using the discontinuous generalization of triangular and quadrilateral Taylor-Hood finite elements, our methods achieves near-optimal L2 convergence in numerical experiments covering both Stokes and Darcy problems. We demonstrate robustness of the method on a variety of 2D numerical benchmark problems, including problems with discontinuous, anisotropic and time dependent permeability fields.
(Less)
- author
- Terschanski, Benjamin
; Klöfkorn, Robert
LU
; Dedner, Andreas
and Kowalski, Julia
- organization
- publishing date
- 2025-07
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Anisotropic permeability, Darcy–Brinkman–Stokes, Darcy–Stokes coupling, Discontinuous Galerkin finite elements (DG-FEM), Porous media flows
- in
- Computer Methods in Applied Mechanics and Engineering
- volume
- 442
- article number
- 117962
- publisher
- Elsevier
- external identifiers
-
- scopus:105004256055
- ISSN
- 0045-7825
- DOI
- 10.1016/j.cma.2025.117962
- language
- English
- LU publication?
- yes
- id
- d24e9331-bdac-4f95-8302-0800a65de647
- date added to LUP
- 2025-08-01 08:53:15
- date last changed
- 2025-08-01 08:54:28
@article{d24e9331-bdac-4f95-8302-0800a65de647,
abstract = {{<p>Hydromechanical models of Darcy–Brinkman–Stokes type consider mass- and momentum conservation of an incompressible fluid on a domain with varying permeability. They include the two important limits of free flow governed by the classical Navier–Stokes equations and porous Darcy flow. The conceptual simplicity makes the model attractive from a modeling perspective, but any numerical solution procedure is challenged by the description of flow domains with different stability requirements. Furthermore, spatial variations in the dominant physics, such as strongly localized rapid variations in permeability adversely affect the conditioning of resulting linear systems. In this publication, we propose a discretization based on mixed discontinuous Galerkin Finite-Elements for the Darcy–Brinkman–Stokes model. The method leverages schemes proposed for the incompressible Navier–Stokes equations and for Darcy flow to obtain a robust solver in both flow limits, as well as for flows that sharply transition from high to low permeability regions. To this end, we introduce a mass-flux stabilization term. Using the discontinuous generalization of triangular and quadrilateral Taylor-Hood finite elements, our methods achieves near-optimal L<sup>2</sup> convergence in numerical experiments covering both Stokes and Darcy problems. We demonstrate robustness of the method on a variety of 2D numerical benchmark problems, including problems with discontinuous, anisotropic and time dependent permeability fields.</p>}},
author = {{Terschanski, Benjamin and Klöfkorn, Robert and Dedner, Andreas and Kowalski, Julia}},
issn = {{0045-7825}},
keywords = {{Anisotropic permeability; Darcy–Brinkman–Stokes; Darcy–Stokes coupling; Discontinuous Galerkin finite elements (DG-FEM); Porous media flows}},
language = {{eng}},
publisher = {{Elsevier}},
series = {{Computer Methods in Applied Mechanics and Engineering}},
title = {{Stable across regimes : A mixed DG method for Darcy–Brinkman–Stokes type flows}},
url = {{http://dx.doi.org/10.1016/j.cma.2025.117962}},
doi = {{10.1016/j.cma.2025.117962}},
volume = {{442}},
year = {{2025}},
}