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A new family of projection schemes for the incompressible Navier–Stokes equations with control of high-frequency damping
Computer Methods in Applied Mechanics and Engineering, Volume: 339, Pages: 160 - 183
Swansea University Authors: Wulf Dettmer , Chennakesava Kadapa , Djordje Peric
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DOI (Published version): 10.1016/j.cma.2018.05.006
Abstract
A simple spatially discrete model problem consisting of mass points and dash-pots is presented which allows for the assessment of the properties of different projection schemes for the solution of the incompressible Navier–Stokes equations. In particular, the temporal accuracy, the stability and the...
Published in: | Computer Methods in Applied Mechanics and Engineering |
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ISSN: | 0045-7825 |
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2018
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URI: | https://cronfa.swan.ac.uk/Record/cronfa39992 |
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2021-01-07T16:31:20.7977171 v2 39992 2018-05-08 A new family of projection schemes for the incompressible Navier–Stokes equations with control of high-frequency damping 30bb53ad906e7160e947fa01c16abf55 0000-0003-0799-4645 Wulf Dettmer Wulf Dettmer true false de01927f8c2c4ad9dcc034c327ac8de1 0000-0001-6092-9047 Chennakesava Kadapa Chennakesava Kadapa true false 9d35cb799b2542ad39140943a9a9da65 0000-0002-1112-301X Djordje Peric Djordje Peric true false 2018-05-08 AERO A simple spatially discrete model problem consisting of mass points and dash-pots is presented which allows for the assessment of the properties of different projection schemes for the solution of the incompressible Navier–Stokes equations. In particular, the temporal accuracy, the stability and the numerical damping are investigated. The present study suggests that it is not possible to formulate a second order accurate projection/pressure-correction scheme which possesses any high-frequency damping. Motivated by this observation two new families of projection schemes are proposed which are developed from the generalised midpoint rule and from the generalised-α method, respectively, and offer control over high-frequency damping. Both schemes are investigated in detail on the basis of the model problem and subsequently implemented in the context of a finite element formulation for the incompressible Navier–Stokes equations. Comprehensive numerical studies of the flow in a lid-driven cavity and the flow around a cylinder are presented. The observations made are in agreement with the conclusions drawn from the model problem. Journal Article Computer Methods in Applied Mechanics and Engineering 339 160 183 0045-7825 Incompressible Navier–Stokes equations; Fractional step method; Projection method; Finite element method; Generalised-alpha method 31 12 2018 2018-12-31 10.1016/j.cma.2018.05.006 COLLEGE NANME Aerospace Engineering COLLEGE CODE AERO Swansea University 2021-01-07T16:31:20.7977171 2018-05-08T09:43:12.0851099 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering A. Lovrić 1 Wulf Dettmer 0000-0003-0799-4645 2 Chennakesava Kadapa 0000-0001-6092-9047 3 Djordje Peric 0000-0002-1112-301X 4 0039992-08052018094434.pdf lovric2018.pdf 2018-05-08T09:44:34.5700000 Output 1562788 application/pdf Accepted Manuscript true 2019-05-26T00:00:00.0000000 true eng |
title |
A new family of projection schemes for the incompressible Navier–Stokes equations with control of high-frequency damping |
spellingShingle |
A new family of projection schemes for the incompressible Navier–Stokes equations with control of high-frequency damping Wulf Dettmer Chennakesava Kadapa Djordje Peric |
title_short |
A new family of projection schemes for the incompressible Navier–Stokes equations with control of high-frequency damping |
title_full |
A new family of projection schemes for the incompressible Navier–Stokes equations with control of high-frequency damping |
title_fullStr |
A new family of projection schemes for the incompressible Navier–Stokes equations with control of high-frequency damping |
title_full_unstemmed |
A new family of projection schemes for the incompressible Navier–Stokes equations with control of high-frequency damping |
title_sort |
A new family of projection schemes for the incompressible Navier–Stokes equations with control of high-frequency damping |
author_id_str_mv |
30bb53ad906e7160e947fa01c16abf55 de01927f8c2c4ad9dcc034c327ac8de1 9d35cb799b2542ad39140943a9a9da65 |
author_id_fullname_str_mv |
30bb53ad906e7160e947fa01c16abf55_***_Wulf Dettmer de01927f8c2c4ad9dcc034c327ac8de1_***_Chennakesava Kadapa 9d35cb799b2542ad39140943a9a9da65_***_Djordje Peric |
author |
Wulf Dettmer Chennakesava Kadapa Djordje Peric |
author2 |
A. Lovrić Wulf Dettmer Chennakesava Kadapa Djordje Peric |
format |
Journal article |
container_title |
Computer Methods in Applied Mechanics and Engineering |
container_volume |
339 |
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160 |
publishDate |
2018 |
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Swansea University |
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0045-7825 |
doi_str_mv |
10.1016/j.cma.2018.05.006 |
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Faculty of Science and Engineering |
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Faculty of Science and Engineering |
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Faculty of Science and Engineering |
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School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering |
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description |
A simple spatially discrete model problem consisting of mass points and dash-pots is presented which allows for the assessment of the properties of different projection schemes for the solution of the incompressible Navier–Stokes equations. In particular, the temporal accuracy, the stability and the numerical damping are investigated. The present study suggests that it is not possible to formulate a second order accurate projection/pressure-correction scheme which possesses any high-frequency damping. Motivated by this observation two new families of projection schemes are proposed which are developed from the generalised midpoint rule and from the generalised-α method, respectively, and offer control over high-frequency damping. Both schemes are investigated in detail on the basis of the model problem and subsequently implemented in the context of a finite element formulation for the incompressible Navier–Stokes equations. Comprehensive numerical studies of the flow in a lid-driven cavity and the flow around a cylinder are presented. The observations made are in agreement with the conclusions drawn from the model problem. |
published_date |
2018-12-31T03:50:51Z |
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1763752491616305152 |
score |
11.037056 |