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Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids

Ya-wei Xie, Michael G. Edwards

Computational Geosciences

Swansea University Author: Michael G. Edwards

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DOI (Published version): 10.1007/s10596-017-9669-5

Abstract

Novel cell-centred finite-volume formulations are presented for incompressible and immiscible two-phase flow with both gravity and capillary pressure effects on structured and unstructured grids. The Darcy-flux is approximated by a control-volume distributed multipoint flux approximation (CVD-MPFA)...

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Published in: Computational Geosciences
ISSN: 1420-0597 1573-1499
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa34232
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spelling 2017-10-03T16:17:42.3733254 v2 34232 2017-06-12 Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids 8903caf3d43fca03602a72ed31d17c59 Michael G. Edwards Michael G. Edwards true false 2017-06-12 FGSEN Novel cell-centred finite-volume formulations are presented for incompressible and immiscible two-phase flow with both gravity and capillary pressure effects on structured and unstructured grids. The Darcy-flux is approximated by a control-volume distributed multipoint flux approximation (CVD-MPFA) coupled with a higher resolution approximation for convective transport. The CVD-MPFA method is used for Darcy-flux approximation involving pressure, gravity, and capillary pressure flux operators. Two IMPES formulations for coupling the pressure equation with fluid transport are presented. The first is based on the classical total velocity Vt fractional flow (Buckley Leverett) formulation, and the second is based on a more recent Va formulation. The CVD-MPFA method is employed for both Vt and Va formulations. The advantages of both coupled formulations are contrasted. The methods are tested on a range of structured and unstructured quadrilateral and triangular grids. The tests show that the resulting methods are found to be comparable for a number of classical cases, including channel flow problems. However, when gravity is present, flow regimes are identified where the Va formulation becomes locally unstable, in contrast to the total velocity formulation. The test cases also show the advantages of the higher resolution method compared to standard first-order single-point upstream weighting. Journal Article Computational Geosciences 1420-0597 1573-1499 Cell-centred finite-volume, Higher resolution method, Two-phase flow, Gravity, Capillary pressure, Vt and Va formulations, CVD, MPFA 31 12 2017 2017-12-31 10.1007/s10596-017-9669-5 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2017-10-03T16:17:42.3733254 2017-06-12T08:30:58.2653386 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Ya-wei Xie 1 Michael G. Edwards 2 0034232-07092017140945.pdf xie2017(2).pdf 2017-09-07T14:09:45.9500000 Output 7292263 application/pdf Version of Record true 2017-09-07T00:00:00.0000000 true eng
title Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids
spellingShingle Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids
Michael G. Edwards
title_short Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids
title_full Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids
title_fullStr Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids
title_full_unstemmed Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids
title_sort Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids
author_id_str_mv 8903caf3d43fca03602a72ed31d17c59
author_id_fullname_str_mv 8903caf3d43fca03602a72ed31d17c59_***_Michael G. Edwards
author Michael G. Edwards
author2 Ya-wei Xie
Michael G. Edwards
format Journal article
container_title Computational Geosciences
publishDate 2017
institution Swansea University
issn 1420-0597
1573-1499
doi_str_mv 10.1007/s10596-017-9669-5
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 Novel cell-centred finite-volume formulations are presented for incompressible and immiscible two-phase flow with both gravity and capillary pressure effects on structured and unstructured grids. The Darcy-flux is approximated by a control-volume distributed multipoint flux approximation (CVD-MPFA) coupled with a higher resolution approximation for convective transport. The CVD-MPFA method is used for Darcy-flux approximation involving pressure, gravity, and capillary pressure flux operators. Two IMPES formulations for coupling the pressure equation with fluid transport are presented. The first is based on the classical total velocity Vt fractional flow (Buckley Leverett) formulation, and the second is based on a more recent Va formulation. The CVD-MPFA method is employed for both Vt and Va formulations. The advantages of both coupled formulations are contrasted. The methods are tested on a range of structured and unstructured quadrilateral and triangular grids. The tests show that the resulting methods are found to be comparable for a number of classical cases, including channel flow problems. However, when gravity is present, flow regimes are identified where the Va formulation becomes locally unstable, in contrast to the total velocity formulation. The test cases also show the advantages of the higher resolution method compared to standard first-order single-point upstream weighting.
published_date 2017-12-31T03:42:27Z
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score 11.037056

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