A conservative hybrid method for darcy flow

Varun Jain; Joël Fisser; Artur Palha; Marc Gerritsma

doi:10.1007/978-3-030-39647-3_16

A conservative hybrid method for darcy flow

Varun Jain^*, Joël Fisser, Artur Palha, Marc Gerritsma

^*Corresponding author for this work

Aerodynamics

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

1 Citation (Scopus)

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Abstract

We present a hybrid mimetic spectral element formulation for Darcy flow. The discrete representations for (1) conservation of mass, and (2) inter-element continuity, are topological relations that lead to sparse matrix systems. These constraints are independent of the element size and shape, and thus invariant under mesh transformations. The resultant algebraic system is extremely sparse even for high degree polynomial basis. Furthermore, the system can be efficiently assembled and solved for each element separately.

Original language	English
Title of host publication	Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference
Editors	Spencer J. Sherwin, Joaquim Peiró, Peter E. Vincent, David Moxey, Christoph Schwab
Publisher	SpringerOpen
Pages	215-227
Number of pages	13
ISBN (Print)	9783030396466
DOIs	https://doi.org/10.1007/978-3-030-39647-3_16
Publication status	Published - 2020
Event	12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018 - London, United Kingdom Duration: 9 Jul 2018 → 13 Jul 2018

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	134
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

Conference

Conference	12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018
Country/Territory	United Kingdom
City	London
Period	9/07/18 → 13/07/18

Access to Document

10.1007/978-3-030-39647-3_16

Jain2020_Chapter_AConservativeHybridMethodForDaFinal published version, 1.79 MBLicence: CC BY

Cite this

Jain, V., Fisser, J., Palha, A., & Gerritsma, M. (2020). A conservative hybrid method for darcy flow. In S. J. Sherwin, J. Peiró, P. E. Vincent, D. Moxey, & C. Schwab (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference (pp. 215-227). (Lecture Notes in Computational Science and Engineering; Vol. 134). SpringerOpen. https://doi.org/10.1007/978-3-030-39647-3_16

Jain, Varun ; Fisser, Joël ; Palha, Artur et al. / A conservative hybrid method for darcy flow. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. editor / Spencer J. Sherwin ; Joaquim Peiró ; Peter E. Vincent ; David Moxey ; Christoph Schwab. SpringerOpen, 2020. pp. 215-227 (Lecture Notes in Computational Science and Engineering).

@inproceedings{e447e0863e504bce87d1f9f9af88df48,

title = "A conservative hybrid method for darcy flow",

abstract = "We present a hybrid mimetic spectral element formulation for Darcy flow. The discrete representations for (1) conservation of mass, and (2) inter-element continuity, are topological relations that lead to sparse matrix systems. These constraints are independent of the element size and shape, and thus invariant under mesh transformations. The resultant algebraic system is extremely sparse even for high degree polynomial basis. Furthermore, the system can be efficiently assembled and solved for each element separately.",

author = "Varun Jain and Jo{\"e}l Fisser and Artur Palha and Marc Gerritsma",

year = "2020",

doi = "10.1007/978-3-030-39647-3_16",

language = "English",

isbn = "9783030396466",

series = "Lecture Notes in Computational Science and Engineering",

publisher = "SpringerOpen",

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editor = "Sherwin, {Spencer J.} and Joaquim Peir{\'o} and Vincent, {Peter E.} and David Moxey and Christoph Schwab",

booktitle = "Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference",

note = "12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018 ; Conference date: 09-07-2018 Through 13-07-2018",

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Jain, V, Fisser, J, Palha, A & Gerritsma, M 2020, A conservative hybrid method for darcy flow. in SJ Sherwin, J Peiró, PE Vincent, D Moxey & C Schwab (eds), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. Lecture Notes in Computational Science and Engineering, vol. 134, SpringerOpen, pp. 215-227, 12th International Conference on Spectral and High-Order Methods, ICOSAHOM 2018, London, United Kingdom, 9/07/18. https://doi.org/10.1007/978-3-030-39647-3_16

A conservative hybrid method for darcy flow. / Jain, Varun; Fisser, Joël; Palha, Artur et al.
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. ed. / Spencer J. Sherwin; Joaquim Peiró; Peter E. Vincent; David Moxey; Christoph Schwab. SpringerOpen, 2020. p. 215-227 (Lecture Notes in Computational Science and Engineering; Vol. 134).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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AU - Jain, Varun

AU - Fisser, Joël

AU - Palha, Artur

AU - Gerritsma, Marc

PY - 2020

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N2 - We present a hybrid mimetic spectral element formulation for Darcy flow. The discrete representations for (1) conservation of mass, and (2) inter-element continuity, are topological relations that lead to sparse matrix systems. These constraints are independent of the element size and shape, and thus invariant under mesh transformations. The resultant algebraic system is extremely sparse even for high degree polynomial basis. Furthermore, the system can be efficiently assembled and solved for each element separately.

AB - We present a hybrid mimetic spectral element formulation for Darcy flow. The discrete representations for (1) conservation of mass, and (2) inter-element continuity, are topological relations that lead to sparse matrix systems. These constraints are independent of the element size and shape, and thus invariant under mesh transformations. The resultant algebraic system is extremely sparse even for high degree polynomial basis. Furthermore, the system can be efficiently assembled and solved for each element separately.

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DO - 10.1007/978-3-030-39647-3_16

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SN - 9783030396466

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BT - Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference

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A2 - Peiró, Joaquim

A2 - Vincent, Peter E.

A2 - Moxey, David

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Jain V, Fisser J, Palha A , Gerritsma M. A conservative hybrid method for darcy flow. In Sherwin SJ, Peiró J, Vincent PE, Moxey D, Schwab C, editors, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 - Selected Papers from the ICOSAHOM Conference. SpringerOpen. 2020. p. 215-227. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-030-39647-3_16

A conservative hybrid method for darcy flow

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