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Stabilization of the Spectral-Element Method in Turbulent Flow Simulations
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-9627-5903
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-7864-3071
2011 (English)In: Spectral and High Order Methods for Partial Differential Equations: Selected papers from the ICOSAHOM '09 conference, June 22-26, Trondheim, Norway, Springer , 2011, 1, 449-458 p.Conference paper, Published paper (Refereed)
Abstract [en]

The effect of over-integration and filter-based stabilization in the spectral-element method is investigated. There is a need to stabilize the SEM for flow problems involving non-smooth solutions, e.g., turbulent flow simulations. In model problems such as the Burgers’ equation (similar to Kirby and Karniadakis, J. Comput. Phys. 191:249–264, 2003) and the scalar transport equation together with full Navier–Stokes simulations it is noticed that over-integration with the full 3/2-rule is not required for stability. The first additional over-integration nodes are the most efficient to remove aliasing errors. Alternatively, filter-based stabilization can in many cases alone help to stabilize the computation.

Place, publisher, year, edition, pages
Springer , 2011, 1. 449-458 p.
Series
Lecture Notes in Computational Science and Engineering, ISSN 1439-7358 ; 76
Keyword [en]
Aliasing error, Burgers' equations, Filter-based, Flow problems, Model problems, Navier Stokes simulation, Non-smooth, Scalar transport equation, SEM, Spectral element method
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-25931DOI: 10.1007/978-3-642-15337-2_43Scopus ID: 2-s2.0-78651526122ISBN: 978-3-642-15336-5 (print)OAI: oai:DiVA.org:kth-25931DiVA: diva2:360905
Conference
8th International Conference on Spectral and High Order Methods, ICOSAHOM'09; Trondheim; Norway; 22 June 2009 through 26 June 2009
Note

QC 20101105

Available from: 2010-11-05 Created: 2010-11-05 Last updated: 2013-11-06Bibliographically approved
In thesis
1. Spectral-element simulations of separated turbulent internal flows
Open this publication in new window or tab >>Spectral-element simulations of separated turbulent internal flows
2009 (English)Licentiate thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Stockholm: US-AB, 2009. vii, 32 p.
Series
Trita-MEK, ISSN 0348-467X ; 2009:13
Keyword
spectral element method, direct numerical simulations (DNS), turbulence, dealiasing, three-dimensional separation, massively parallel simulations
Identifiers
urn:nbn:se:kth:diva-11643 (URN)978-91-7415-506-8 (ISBN)
Presentation
2009-12-15, E3, Osquars Backe 14, Stockholm, 10:15 (English)
Opponent
Supervisors
Note
QC 20101105Available from: 2009-11-27 Created: 2009-11-27 Last updated: 2010-11-05Bibliographically approved
2. Spectral-element simulations of turbulent wall-bounded flows including transition and separation
Open this publication in new window or tab >>Spectral-element simulations of turbulent wall-bounded flows including transition and separation
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The spectral-element method (SEM) is used to study wall-bounded turbulent flowsin moderately complex geometries. The first part of the thesis is devoted to simulations of canonical flow cases, such as temporal K-type transitionand turbulent channel flow, to investigate general resolution requirements and computational efficiency of the numerical code nek5000. Large-eddy simulation (LES) is further performed of a plane asymmetric diffuser flow with an opening angle of 8.5 degrees, featuring turbulent flow separation. Good agreement with numerical studies of Herbst (2007) is obtained, and it is concluded that the use of a high-order method is advantageous for flows featuring pressure-induced separation. Moreover, it is shown, both a priori on simpler model problems and a posteriori using the full Navier--Stokes equations, that the numerical instability associated with SEM at high Reynolds numbers is cured either by employing over-integration (dealiasing) or a filter-based stabilisation, thus rendering simulations of moderate to high Reynolds number flows possible.

The second part of the thesis is devoted to the first direct numerical simulation (DNS) of a truly three-dimensional, turbulent and separated diffuser flow at Re = 10 000 (based on bulk velocity and inflow-duct height), experimentally investigated by Cherry et al. (2008). The massively parallel capabilities of the spectral-element method are exploited by running the simulations on up to 32 768 processors. Very good agreement with experimental mean flow data is obtained and it is thus shown that well-resolved simulations of complex turbulent flows with high accuracy are possible at realistic Reynolds numberseven in complicated geometries. An explanation for the discovered asymmetry of the mean separated flow is provided and itis demonstrated that a large-scale quasi-periodic motion is present in the diffuser.

In addition, a new diagnostic measure, based on the maximum vorticity stretching component in every spatial point, is designed and tested in a number of turbulent and transitional flows. Finally, Koopman mode decomposition is performed of a minimal channel flow and compared to classical proper orthogonal decomposition (POD).

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. ix, 81 p.
Series
Trita-MEK, ISSN 0348-467X ; 2011:15
Keyword
spectral-element method, direct numerical simulation (DNS), large-eddy simulation (LES), turbulence, transition, over-integration, three-dimensional separation, massively parallel simulations, proper orthogonal decomposition (POD), Koopman modes, vorticity stretching, coherence
National Category
Engineering and Technology
Research subject
SRA - E-Science (SeRC)
Identifiers
urn:nbn:se:kth:diva-50294 (URN)978-91-7501-178-3 (ISBN)
Public defence
2011-12-16, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:15 (English)
Opponent
Supervisors
Funder
Swedish Research CouncilSwedish e‐Science Research Center
Note
QC 20111206Available from: 2011-12-06 Created: 2011-12-04 Last updated: 2012-05-24Bibliographically approved

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Schlatter, PhilippHenningson, Dan S.

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