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Multiscale Finite-Volume CVD-MPFA Formulations on Structured and Unstructured Grids

Elliot Parramore, Michael G. Edwards, Mayur Pal, Sadok Lamine

Multiscale Modeling & Simulation, Volume: 14, Issue: 2, Pages: 559 - 594

Swansea University Author: Michael G. Edwards

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DOI (Published version): 10.1137/140953691

Abstract

This paper presents the development of finite-volume multiscale methods for quadrilateral and triangular unstructured grids. Families of Darcy-flux approximations have been developed for consistent approximation of the general tensor pressure equation arising from Darcy's law together with mass...

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Published in: Multiscale Modeling & Simulation
ISSN: 1540-3459 1540-3467
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa30223
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spelling 2018-05-13T18:12:23.9855875 v2 30223 2016-09-26 Multiscale Finite-Volume CVD-MPFA Formulations on Structured and Unstructured Grids 8903caf3d43fca03602a72ed31d17c59 Michael G. Edwards Michael G. Edwards true false 2016-09-26 FGSEN This paper presents the development of finite-volume multiscale methods for quadrilateral and triangular unstructured grids. Families of Darcy-flux approximations have been developed for consistent approximation of the general tensor pressure equation arising from Darcy's law together with mass conservation. The schemes are control-volume distributed (CVD) with flow variables and rock properties sharing the same control-volume location and are comprised of a multipoint flux family formulation (CVD-MPFA). The schemes are used to develop a CVD-MPFA based multiscale finite-volume (MSFV) formulation applicable to both structured and unstructured grids in two dimensions. The basis functions are a key component of the MSFV method, and are a set of local solutions, usually defined subject to Dirichlet boundary conditions. A generalization of the Cartesian grid Dirichlet basis functions described in [P. Jenny, S. H. Lee, and H. A. Tchelepi, J. Comput. Phys., 187 (2003), pp. 47--67] is presented here for unstructured grids. Whilst the transition from a Cartesian grid to an unstructured grid is largely successful, use of Dirichlet basis functions can still lead to pressure fields that exhibit spurious oscillations in areas of strong heterogeneity. New basis functions are proposed in an attempt to improve the pressure field solutions where Neumann boundary conditions are imposed almost everywhere, except corners which remain specified by Dirichlet values. Journal Article Multiscale Modeling & Simulation 14 2 559 594 1540-3459 1540-3467 multiscale finite-volume (MSFV) methods, control-volume distributed multipoint flux approximations (CVD-MPFA) 12 4 2016 2016-04-12 10.1137/140953691 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2018-05-13T18:12:23.9855875 2016-09-26T22:27:52.5017686 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Elliot Parramore 1 Michael G. Edwards 2 Mayur Pal 3 Sadok Lamine 4 0030223-27022017154459.pdf Multiscale_Finitevolume_CVDMPFA_Formulations_on_Structured_Unstructured_Grids.pdf 2017-02-27T15:44:59.2330000 Output 8066040 application/pdf Accepted Manuscript true 2017-02-27T00:00:00.0000000 false eng
title Multiscale Finite-Volume CVD-MPFA Formulations on Structured and Unstructured Grids
spellingShingle Multiscale Finite-Volume CVD-MPFA Formulations on Structured and Unstructured Grids
Michael G. Edwards
title_short Multiscale Finite-Volume CVD-MPFA Formulations on Structured and Unstructured Grids
title_full Multiscale Finite-Volume CVD-MPFA Formulations on Structured and Unstructured Grids
title_fullStr Multiscale Finite-Volume CVD-MPFA Formulations on Structured and Unstructured Grids
title_full_unstemmed Multiscale Finite-Volume CVD-MPFA Formulations on Structured and Unstructured Grids
title_sort Multiscale Finite-Volume CVD-MPFA Formulations on Structured and Unstructured Grids
author_id_str_mv 8903caf3d43fca03602a72ed31d17c59
author_id_fullname_str_mv 8903caf3d43fca03602a72ed31d17c59_***_Michael G. Edwards
author Michael G. Edwards
author2 Elliot Parramore
Michael G. Edwards
Mayur Pal
Sadok Lamine
format Journal article
container_title Multiscale Modeling & Simulation
container_volume 14
container_issue 2
container_start_page 559
publishDate 2016
institution Swansea University
issn 1540-3459
1540-3467
doi_str_mv 10.1137/140953691
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
active_str 0
description This paper presents the development of finite-volume multiscale methods for quadrilateral and triangular unstructured grids. Families of Darcy-flux approximations have been developed for consistent approximation of the general tensor pressure equation arising from Darcy's law together with mass conservation. The schemes are control-volume distributed (CVD) with flow variables and rock properties sharing the same control-volume location and are comprised of a multipoint flux family formulation (CVD-MPFA). The schemes are used to develop a CVD-MPFA based multiscale finite-volume (MSFV) formulation applicable to both structured and unstructured grids in two dimensions. The basis functions are a key component of the MSFV method, and are a set of local solutions, usually defined subject to Dirichlet boundary conditions. A generalization of the Cartesian grid Dirichlet basis functions described in [P. Jenny, S. H. Lee, and H. A. Tchelepi, J. Comput. Phys., 187 (2003), pp. 47--67] is presented here for unstructured grids. Whilst the transition from a Cartesian grid to an unstructured grid is largely successful, use of Dirichlet basis functions can still lead to pressure fields that exhibit spurious oscillations in areas of strong heterogeneity. New basis functions are proposed in an attempt to improve the pressure field solutions where Neumann boundary conditions are imposed almost everywhere, except corners which remain specified by Dirichlet values.
published_date 2016-04-12T03:36:51Z
_version_ 1763751610805125120
score 11.037603

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