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A new high-order method for the simulation of incompressible wall-bounded turbulent flows
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Mechanics of Industrial Processes. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-9627-5903
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-9819-2906
KTH, School of Engineering Sciences (SCI), Mechanics, Turbulence. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-2711-4687
2014 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 272, 108-126 p.Article in journal (Refereed) Published
Abstract [en]

A new high-order method for the accurate simulation of incompressible wall-bounded flows is presented. In the stream- and spanwise directions the discretisation is performed by standard Fourier series, while in the wall-normal direction the method combines high-order collocated compact finite differences with the influence matrix method to calculate the pressure boundary conditions that render the velocity field exactly divergence-free. The main advantage over Chebyshev collocation is that in wall-normal direction, the grid can be chosen freely and thus excessive clustering near the wall is avoided. This can be done while maintaining the high-order approximation as offered by compact finite differences. The discrete Poisson equation is solved in a novel way that avoids any full matrices and thus improves numerical efficiency. Both explicit and implicit discretisations of the viscous terms are described, with the implicit method being more complex, but also having a wider range of applications. The method is validated by simulating two-dimensional Tollmien-Schlichting waves, forced transition in turbulent channel flow, and fully turbulent channel flow at friction Reynolds number Re-tau = 395, and comparing our data with analytical and existing numerical results. In all cases, the results show excellent agreement showing that the method simulates all physical processes correctly.

Place, publisher, year, edition, pages
Academic Press , 2014. Vol. 272, 108-126 p.
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-142392DOI: 10.1016/j.jcp.2014.04.034ISI: 000336620900006Scopus ID: 2-s2.0-84899836589OAI: oai:DiVA.org:kth-142392DiVA: diva2:700088
Funder
Swedish Research Council
Note

QC 20140702

Available from: 2014-03-03 Created: 2014-03-03 Last updated: 2017-12-05Bibliographically approved
In thesis
1. A new high-order method for direct numerical simulations of turbulent wall-bounded flows
Open this publication in new window or tab >>A new high-order method for direct numerical simulations of turbulent wall-bounded flows
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

A new method to perform direct numerical simulations of wall-bounded flows has been developed and implemented. The method uses high-order compact finite differences in wall-normal (for channel flow) or radial direction (for pipe flow) on a collocated grid, which gives high-accuracy results without the effectfof filtering caused by frequent interpolation as required on a staggered grid. The use of compact finite differences means that extreme clustering near the wall leading to small time steps in high-Reynolds number simulations is avoided. The influence matrix method is used to ensure a completely divergence-freesolution and all systems of equations are solved in banded form, which ensures an effcient solution procedure with low requirements for data storage. The method is unique in the sense that exactly divergence-free solutions on collocated meshes are calculated using arbitrary dffierence matrices.

The code is validated for two flow cases, i.e. turbulent channel and turbulent pipe flow at relatively low Reynolds number. All tests show excellent agreement with analytical and existing results, confirming the accuracy and robustness ofthe method. The next step is to eciently parallelise the code so that high-Reynolds number simulations at high resolution can be performed.

We furthermore investigated rare events occurring in the near-wall region of turbulent wall-bounded flows. We find that negative streamwise velocities and extreme wall-normal velocity uctuations are found rarely (on the order of 0:01%), and that they occur more frequently at higher Reynolds number. These events are caused by strong vortices lying further away from the wall and it appears that these events are universal for wall-bounded flows.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. xii, 40 p.
Keyword
Incompressible wall-bounded flows, direct numerical simulations, high-order, compact finite differences, collocated grid, influence matrix method
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-142374 (URN)
Public defence
2014-03-21, Kollegiesalen, Brinellvägen 8, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20150303

Available from: 2014-03-03 Created: 2014-03-03 Last updated: 2014-03-03Bibliographically approved

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Schlatter, PhilippBrethouwer, GeertJohansson, Arne

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