Abstract
We present an LES-type variational multiscale theory of turbulence. Our approach derives completely from the incompressible Navier–Stokes equations and does not employ any ad hoc devices, such as eddy viscosities. We tested the formulation on a turbulent channel flow. In the calculations, we employed quadratic and cubic B-Splines. The numerical results are very good and confirm the viability of the theoretical framework. (This paper is excerpted from Bazilevs et al. [1], which is a much more comprehensive presentation of the theory, algorithms, implementation, and numerical studies. The reader is referred to it for further elaboration and many additional details.)
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Y. Bazilevs, V.M. Calo, J.A. Cottrel, T.J.R. Hughes, A. Reali, and G. Scovazzi. Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Computer Methods in Applied Mechanics and Engineering, 197:173–201, 2007.
Y. Bazilevs and T.J.R. Hughes. Weak imposition of Dirichlet boundary conditions in fluid mechanics. Computers and Fluids, 36:12–26, 2007.
J. Holmen, T.J.R. Hughes, A.A. Oberai, and G.N. Wells. Sensitivity of the scale partition for variational multiscale LES of channel flow. Physics of Fluids, 16:824–827, 2004.
T. J. R. Hughes, G. Feijóo., L. Mazzei, and J. B. Quincy. The variational multiscale method – A paradigm for computational mechanics. Computer Methods in Applied Mechanics and Engineering, 166:3–24, 1998.
T.J.R. Hughes, A.A. Oberai, and L. Mazzei. Large-eddy simulation of turbulent channel flows by the variational multiscale method. Physics of Fluids, 13: 1784–1799, 2001.
T.J.R. Hughes and G. Sangalli. Variational multiscale analysis: the fine-scale Green’s function, projection, optimization, localization, and stabilized methods. SIAM Journal of Numerical Analysis, 45:539–557, 2007.
T.J.R. Hughes, G. Scovazzi, and L.P. Franca. Multiscale and stabilized methods. In E. Stein, R. de Borst, and T. J. R. Hughes, editors, Encyclopedia of Computational Mechanics, Vol. 3, Computational Fluid Dynamics, chapter 2. Wiley, 2004.
R. Moser, J. Kim, and R. Mansour. DNS of turbulent channel flow up to Re = 590. Physics of Fluids, 11:943–945, 1999.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media B.V.
About this paper
Cite this paper
Bazilevs, Y., Calo, V.M., Hughes, T.J.R., Scovazzi, G. (2010). Variational Multiscale Theory of LES Turbulence Modeling. In: Armenio, V., Geurts, B., Fröhlich, J. (eds) Direct and Large-Eddy Simulation VII. ERCOFTAC Series, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3652-0_16
Download citation
DOI: https://doi.org/10.1007/978-90-481-3652-0_16
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-3651-3
Online ISBN: 978-90-481-3652-0
eBook Packages: EngineeringEngineering (R0)