Three-Dimensional Stabilized Mixed Galerkin Method for Darcy Flow

Shahab U. Ansari; Masroor Hussain; Suleman Mazhar; Ahmar Rashid; S. M. Ahmad

doi:10.1109/FIT.2015.67

Three-Dimensional Stabilized Mixed Galerkin Method for Darcy Flow

Shahab U. Ansari
, Masroor Hussain
, Suleman Mazhar
, Ahmar Rashid
, S. M. Ahmad

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

Two-dimensional stabilized mixed Galerkin method using self-adjoint residual of the momentum equation (Darcy's law) has been previously implemented. In the present work, we are extending the two-dimensional stabilized model by incorporating the third dimension into the mathematical formulation. This extended stabilized mixed model would be able to accurately simulate more realistic flow of incompressible fluid through porous media. In the experimentation, the media is assumed homogeneous and the flow is considered laminar. The study shows that the numerically computed Darcy pressure and the velocity using hexahedral elements are comparable to the analytical solutions. In addition, the approximations converge to the exact solutions as the size of the elements decreases.

Original language	English
Title of host publication	Proceedings - 2015 13th International Conference on Frontiers of Information Technology, FIT 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	104-108
Number of pages	5
ISBN (Electronic)	9781467396660
DOIs	https://doi.org/10.1109/FIT.2015.67
State	Published - 26 Feb 2016
Externally published	Yes
Event	13th International Conference on Frontiers of Information Technology, FIT 2015 - Islamabad, Pakistan Duration: 14 Dec 2015 → 16 Dec 2015

Publication series

Name	Proceedings - 2015 13th International Conference on Frontiers of Information Technology, FIT 2015

Conference

Conference	13th International Conference on Frontiers of Information Technology, FIT 2015
Country/Territory	Pakistan
City	Islamabad
Period	14/12/15 → 16/12/15

Bibliographical note

Publisher Copyright:
© 2015 IEEE.

Keywords

Darcy flow
Galerkin method
Stabilized mixed method

ASJC Scopus subject areas

Health Informatics
Computer Science Applications
Signal Processing

Access to Document

10.1109/FIT.2015.67

Cite this

Ansari, S. U., Hussain, M., Mazhar, S., Rashid, A., & Ahmad, S. M. (2016). Three-Dimensional Stabilized Mixed Galerkin Method for Darcy Flow. In Proceedings - 2015 13th International Conference on Frontiers of Information Technology, FIT 2015 (pp. 104-108). Article 7420984 (Proceedings - 2015 13th International Conference on Frontiers of Information Technology, FIT 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/FIT.2015.67

Ansari, Shahab U. ; Hussain, Masroor ; Mazhar, Suleman et al. / Three-Dimensional Stabilized Mixed Galerkin Method for Darcy Flow. Proceedings - 2015 13th International Conference on Frontiers of Information Technology, FIT 2015. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 104-108 (Proceedings - 2015 13th International Conference on Frontiers of Information Technology, FIT 2015).

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title = "Three-Dimensional Stabilized Mixed Galerkin Method for Darcy Flow",

abstract = "Two-dimensional stabilized mixed Galerkin method using self-adjoint residual of the momentum equation (Darcy's law) has been previously implemented. In the present work, we are extending the two-dimensional stabilized model by incorporating the third dimension into the mathematical formulation. This extended stabilized mixed model would be able to accurately simulate more realistic flow of incompressible fluid through porous media. In the experimentation, the media is assumed homogeneous and the flow is considered laminar. The study shows that the numerically computed Darcy pressure and the velocity using hexahedral elements are comparable to the analytical solutions. In addition, the approximations converge to the exact solutions as the size of the elements decreases.",

keywords = "Darcy flow, Galerkin method, Stabilized mixed method",

author = "Ansari, \{Shahab U.\} and Masroor Hussain and Suleman Mazhar and Ahmar Rashid and Ahmad, \{S. M.\}",

note = "Publisher Copyright: {\textcopyright} 2015 IEEE.; 13th International Conference on Frontiers of Information Technology, FIT 2015 ; Conference date: 14-12-2015 Through 16-12-2015",

year = "2016",

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doi = "10.1109/FIT.2015.67",

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series = "Proceedings - 2015 13th International Conference on Frontiers of Information Technology, FIT 2015",

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Ansari, SU, Hussain, M, Mazhar, S, Rashid, A & Ahmad, SM 2016, Three-Dimensional Stabilized Mixed Galerkin Method for Darcy Flow. in Proceedings - 2015 13th International Conference on Frontiers of Information Technology, FIT 2015., 7420984, Proceedings - 2015 13th International Conference on Frontiers of Information Technology, FIT 2015, Institute of Electrical and Electronics Engineers Inc., pp. 104-108, 13th International Conference on Frontiers of Information Technology, FIT 2015, Islamabad, Pakistan, 14/12/15. https://doi.org/10.1109/FIT.2015.67

Three-Dimensional Stabilized Mixed Galerkin Method for Darcy Flow. / Ansari, Shahab U.; Hussain, Masroor; Mazhar, Suleman et al.
Proceedings - 2015 13th International Conference on Frontiers of Information Technology, FIT 2015. Institute of Electrical and Electronics Engineers Inc., 2016. p. 104-108 7420984 (Proceedings - 2015 13th International Conference on Frontiers of Information Technology, FIT 2015).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Three-Dimensional Stabilized Mixed Galerkin Method for Darcy Flow

AU - Ansari, Shahab U.

AU - Hussain, Masroor

AU - Mazhar, Suleman

AU - Rashid, Ahmar

AU - Ahmad, S. M.

PY - 2016/2/26

Y1 - 2016/2/26

N2 - Two-dimensional stabilized mixed Galerkin method using self-adjoint residual of the momentum equation (Darcy's law) has been previously implemented. In the present work, we are extending the two-dimensional stabilized model by incorporating the third dimension into the mathematical formulation. This extended stabilized mixed model would be able to accurately simulate more realistic flow of incompressible fluid through porous media. In the experimentation, the media is assumed homogeneous and the flow is considered laminar. The study shows that the numerically computed Darcy pressure and the velocity using hexahedral elements are comparable to the analytical solutions. In addition, the approximations converge to the exact solutions as the size of the elements decreases.

AB - Two-dimensional stabilized mixed Galerkin method using self-adjoint residual of the momentum equation (Darcy's law) has been previously implemented. In the present work, we are extending the two-dimensional stabilized model by incorporating the third dimension into the mathematical formulation. This extended stabilized mixed model would be able to accurately simulate more realistic flow of incompressible fluid through porous media. In the experimentation, the media is assumed homogeneous and the flow is considered laminar. The study shows that the numerically computed Darcy pressure and the velocity using hexahedral elements are comparable to the analytical solutions. In addition, the approximations converge to the exact solutions as the size of the elements decreases.

KW - Darcy flow

KW - Galerkin method

KW - Stabilized mixed method

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M3 - Conference contribution

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T3 - Proceedings - 2015 13th International Conference on Frontiers of Information Technology, FIT 2015

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BT - Proceedings - 2015 13th International Conference on Frontiers of Information Technology, FIT 2015

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Ansari SU, Hussain M, Mazhar S, Rashid A, Ahmad SM. Three-Dimensional Stabilized Mixed Galerkin Method for Darcy Flow. In Proceedings - 2015 13th International Conference on Frontiers of Information Technology, FIT 2015. Institute of Electrical and Electronics Engineers Inc. 2016. p. 104-108. 7420984. (Proceedings - 2015 13th International Conference on Frontiers of Information Technology, FIT 2015). doi: 10.1109/FIT.2015.67

Three-Dimensional Stabilized Mixed Galerkin Method for Darcy Flow

Abstract

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Bibliographical note

Keywords

ASJC Scopus subject areas

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