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Multidimensional upwind schemes and higher resolution methods for three-component two-phase systems including gravity driven flow in porous media on unstructured grids

Sadok Lamine, Michael G. Edwards

Computer Methods in Applied Mechanics and Engineering, Volume: 292, Pages: 171 - 194

Swansea University Author: Michael G. Edwards

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DOI (Published version): 10.1016/j.cma.2014.12.022

Abstract

Standard reservoir simulation schemes employ single-point upstream weighting for approximation of the convective fluxes when multiple phases or components are present. These schemes introduce both coordinate-line numerical diffusion and crosswind diffusion into the solution that is grid and geometry...

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Published in: Computer Methods in Applied Mechanics and Engineering
Published: 2015
URI: https://cronfa.swan.ac.uk/Record/cronfa21408
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spelling 2019-09-07T18:00:38.4602098 v2 21408 2015-05-14 Multidimensional upwind schemes and higher resolution methods for three-component two-phase systems including gravity driven flow in porous media on unstructured grids 8903caf3d43fca03602a72ed31d17c59 Michael G. Edwards Michael G. Edwards true false 2015-05-14 FGSEN Standard reservoir simulation schemes employ single-point upstream weighting for approximation of the convective fluxes when multiple phases or components are present. These schemes introduce both coordinate-line numerical diffusion and crosswind diffusion into the solution that is grid and geometry dependent.Families of locally conservative multidimensional upwind schemes are presented for essentially hyperbolic three-component two-phase flow systems of conservation laws in porous media including counter current gravity flow on unstructured grids. The multidimensional methods employ cell-based tracing, which involves tracing characteristic wave directions over each control-volume subquadrant. The multidimensional methods reduce crosswind diffusion inherent in standard methods for convective flow approximation in porous media. The schemes are coupled with continuous Darcy-flux approximations resulting from the elliptic pressure equation on unstructured grids.Characteristic upwind approximations are proposed and compared with the classical upstream weighting schemes for cases including gravity segregated flow. When dealing with systems of hyperbolic equations, upwind characteristic wave decomposition is used for wave tracing. The multidimensional upwind cell-based tracing formulations are designed for unstructured grids (and include structured grids by default) and are stable subject to conditions on the tracing direction and CFL number and satisfy a local maximum principle that ensures solutions are free of spurious oscillations.Benefits of the resulting schemes are demonstrated for two-phase flow and a three-component two-phase flow system including gravity segregated flow. The multidimensional cell based schemes are shown to reduce crosswind diffusion induced by standard upwind methods, and prove to be particularly effective when flow is strongly non-aligned with the grid, leading to improved resolution of numerical saturation and concentration fronts. Extension of higher order schemes to a three-component two-phase flow systems of conservation laws on unstructured grids is also presented, which provides a significant improvement in flow resolution for the system cases. Comparison is drawn between the methods. Journal Article Computer Methods in Applied Mechanics and Engineering 292 171 194 1 8 2015 2015-08-01 10.1016/j.cma.2014.12.022 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2019-09-07T18:00:38.4602098 2015-05-14T13:08:42.8807819 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Sadok Lamine 1 Michael G. Edwards 2 0021408-31032016230336.pdf CMAME_MultiD_Systems.pdf 2016-03-31T23:03:36.9900000 Output 2363009 application/pdf Submitted Manuscript Under Review true 2016-07-20T00:00:00.0000000 © 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ true
title Multidimensional upwind schemes and higher resolution methods for three-component two-phase systems including gravity driven flow in porous media on unstructured grids
spellingShingle Multidimensional upwind schemes and higher resolution methods for three-component two-phase systems including gravity driven flow in porous media on unstructured grids
Michael G. Edwards
title_short Multidimensional upwind schemes and higher resolution methods for three-component two-phase systems including gravity driven flow in porous media on unstructured grids
title_full Multidimensional upwind schemes and higher resolution methods for three-component two-phase systems including gravity driven flow in porous media on unstructured grids
title_fullStr Multidimensional upwind schemes and higher resolution methods for three-component two-phase systems including gravity driven flow in porous media on unstructured grids
title_full_unstemmed Multidimensional upwind schemes and higher resolution methods for three-component two-phase systems including gravity driven flow in porous media on unstructured grids
title_sort Multidimensional upwind schemes and higher resolution methods for three-component two-phase systems including gravity driven flow in porous media on unstructured grids
author_id_str_mv 8903caf3d43fca03602a72ed31d17c59
author_id_fullname_str_mv 8903caf3d43fca03602a72ed31d17c59_***_Michael G. Edwards
author Michael G. Edwards
author2 Sadok Lamine
Michael G. Edwards
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 292
container_start_page 171
publishDate 2015
institution Swansea University
doi_str_mv 10.1016/j.cma.2014.12.022
college_str Faculty of Science and Engineering
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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
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description Standard reservoir simulation schemes employ single-point upstream weighting for approximation of the convective fluxes when multiple phases or components are present. These schemes introduce both coordinate-line numerical diffusion and crosswind diffusion into the solution that is grid and geometry dependent.Families of locally conservative multidimensional upwind schemes are presented for essentially hyperbolic three-component two-phase flow systems of conservation laws in porous media including counter current gravity flow on unstructured grids. The multidimensional methods employ cell-based tracing, which involves tracing characteristic wave directions over each control-volume subquadrant. The multidimensional methods reduce crosswind diffusion inherent in standard methods for convective flow approximation in porous media. The schemes are coupled with continuous Darcy-flux approximations resulting from the elliptic pressure equation on unstructured grids.Characteristic upwind approximations are proposed and compared with the classical upstream weighting schemes for cases including gravity segregated flow. When dealing with systems of hyperbolic equations, upwind characteristic wave decomposition is used for wave tracing. The multidimensional upwind cell-based tracing formulations are designed for unstructured grids (and include structured grids by default) and are stable subject to conditions on the tracing direction and CFL number and satisfy a local maximum principle that ensures solutions are free of spurious oscillations.Benefits of the resulting schemes are demonstrated for two-phase flow and a three-component two-phase flow system including gravity segregated flow. The multidimensional cell based schemes are shown to reduce crosswind diffusion induced by standard upwind methods, and prove to be particularly effective when flow is strongly non-aligned with the grid, leading to improved resolution of numerical saturation and concentration fronts. Extension of higher order schemes to a three-component two-phase flow systems of conservation laws on unstructured grids is also presented, which provides a significant improvement in flow resolution for the system cases. Comparison is drawn between the methods.
published_date 2015-08-01T03:25:23Z
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