A polytopal method for the Brinkman problem robust in all regimes

Daniele A. Di Pietro; Jérôme Droniou

doi:10.1016/j.cma.2023.115981

A polytopal method for the Brinkman problem robust in all regimes

Daniele A. Di Pietro
, Jérôme Droniou

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

9 Citations (Scopus)

Abstract

In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meaning of a friction coefficient) and supports general meshes as well as arbitrary approximation orders. The method is obtained combining ideas from the Hybrid High-Order and Discrete de Rham methods, and its robustness rests on a potential reconstruction and stabilisation terms that change in nature according to the value of the local friction coefficient. We derive error estimates that, thanks to the presence of cut-off factors, are valid across all the regimes and provide extensive numerical validation.

Original language	English
Article number	115981
Number of pages	23
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	409
DOIs	https://doi.org/10.1016/j.cma.2023.115981
Publication status	Published - 1 May 2023

Keywords

Brinkman
Darcy
Discrete de Rham methods
Hybrid high-order methods
Stokes

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10.1016/j.cma.2023.115981

Cite this

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title = "A polytopal method for the Brinkman problem robust in all regimes",

abstract = "In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meaning of a friction coefficient) and supports general meshes as well as arbitrary approximation orders. The method is obtained combining ideas from the Hybrid High-Order and Discrete de Rham methods, and its robustness rests on a potential reconstruction and stabilisation terms that change in nature according to the value of the local friction coefficient. We derive error estimates that, thanks to the presence of cut-off factors, are valid across all the regimes and provide extensive numerical validation.",

keywords = "Brinkman, Darcy, Discrete de Rham methods, Hybrid high-order methods, Stokes",

author = "\{Di Pietro\}, \{Daniele A.\} and J{\'e}r{\^o}me Droniou",

note = "Funding Information: This research received support from the ANR “NEMESIS”, France ( ANR-20-MRS2-0004 ) and the Australian Research Council{\textquoteright}s Discovery Projects funding scheme ( DP210103092 ). The authors would also like to thank Ricardo Ruiz-Baier for sharing Gmsh geometry files at the source of the tests in Section 4.3 . Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

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doi = "10.1016/j.cma.2023.115981",

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T1 - A polytopal method for the Brinkman problem robust in all regimes

AU - Di Pietro, Daniele A.

AU - Droniou, Jérôme

N1 - Funding Information: This research received support from the ANR “NEMESIS”, France ( ANR-20-MRS2-0004 ) and the Australian Research Council’s Discovery Projects funding scheme ( DP210103092 ). The authors would also like to thank Ricardo Ruiz-Baier for sharing Gmsh geometry files at the source of the tests in Section 4.3 . Publisher Copyright: © 2023 Elsevier B.V.

PY - 2023/5/1

Y1 - 2023/5/1

N2 - In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meaning of a friction coefficient) and supports general meshes as well as arbitrary approximation orders. The method is obtained combining ideas from the Hybrid High-Order and Discrete de Rham methods, and its robustness rests on a potential reconstruction and stabilisation terms that change in nature according to the value of the local friction coefficient. We derive error estimates that, thanks to the presence of cut-off factors, are valid across all the regimes and provide extensive numerical validation.

AB - In this work we develop a discretisation method for the Brinkman problem that is uniformly well-behaved in all regimes (as identified by a local dimensionless number with the meaning of a friction coefficient) and supports general meshes as well as arbitrary approximation orders. The method is obtained combining ideas from the Hybrid High-Order and Discrete de Rham methods, and its robustness rests on a potential reconstruction and stabilisation terms that change in nature according to the value of the local friction coefficient. We derive error estimates that, thanks to the presence of cut-off factors, are valid across all the regimes and provide extensive numerical validation.

KW - Brinkman

KW - Darcy

KW - Discrete de Rham methods

KW - Hybrid high-order methods

KW - Stokes

UR - https://www.scopus.com/pages/publications/85149926449

U2 - 10.1016/j.cma.2023.115981

DO - 10.1016/j.cma.2023.115981

M3 - Article

AN - SCOPUS:85149926449

SN - 0045-7825

VL - 409

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

M1 - 115981

ER -

A polytopal method for the Brinkman problem robust in all regimes

Abstract

Keywords

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Interface-aware numerical methods for stochastic inverse problems

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