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Wavelet-based adaptive simulations of three-dimensional flow past a square cylinder

Published online by Cambridge University Press:  30 April 2014

Giuliano De Stefano  and
Oleg V. Vasilyev
Giuliano De Stefano
Affiliation:
Dipartimento di Ingegneria Industriale e dell’Informazione, Seconda Università di Napoli, I 81031 Aversa, Italy
Oleg V. Vasilyev*
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309, USA
*
†Email address for correspondence: oleg.vasilyev@colorado.edu
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Abstract

The wavelet-based eddy capturing approach is extended to three-dimensional bluff body flows, where the flow geometry is enforced through Brinkman volume penalization. The wavelet-collocation/volume-penalization combined method is applied to the simulation of vortex shedding flow behind an isolated stationary prism with square cross-section. Wavelet-based direct numerical simulation is conducted at low supercritical Reynolds number, where the wake develops fundamental three-dimensional flow structures, while wavelet-based adaptive large-eddy simulation supplied with the one-equation localized dynamic kinetic-energy-based model is performed at moderately high Reynolds number. The present results are in general agreement with experimental findings and numerical solutions provided by classical non-adaptive methods. This study demonstrates that the proposed hybrid methodology for modelling bluff body flows is feasible, accurate and efficient.

JFM classification

Mathematical Foundations: Computational methods Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 748 , 10 June 2014 , pp. 433 - 456
Copyright
© 2014 Cambridge University Press 

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References

Angot, P., Bruneau, C. -H. & Fabrie, P. 1999 A penalization method to take into account obstacles in incompressible viscous flows. Numer. Math. 81, 497–520.CrossRefGoogle Scholar
Brun, C., Aubrun, S., Goossens, T. & Ravier, Ph. 2008 Coherent structures and their frequency signature in the separated shear layer on the sides of a square cylinder. Flow Turbul. Combust. 81, 97–114.CrossRefGoogle Scholar
Carbou, G. & Fabrie, P. 2003 Boundary layer for a penalization method for viscous incompressible flow. Adv. Difference. Equ. 8 (12), 1409–1532.Google Scholar
De Stefano, G., Denaro, F. M. & Riccardi, G. 1998 Analysis of 3D backward-facing step incompressible flows via a local average-based numerical procedure. Intl J. Numer. Meth. Fluids 28, 1073–1091.3.0.CO;2-H>CrossRefGoogle Scholar
De Stefano, G. & Vasilyev, O. V. 2010 Stochastic coherent adaptive large eddy simulation of forced isotropic turbulence. J. Fluid Mech. 646, 453–470.CrossRefGoogle Scholar
De Stefano, G. & Vasilyev, O. V. 2012 A fully adaptive wavelet-based approach to homogeneous turbulence simulation. J. Fluid Mech. 695, 149–172.CrossRefGoogle Scholar
De Stefano, G., Vasilyev, O. V. & Goldstein, D. E. 2008 Localized dynamic kinetic energy-based models for stochastic coherent adaptive large eddy simulation. Phys. Fluids 20 (4), 045102, 1–14.CrossRefGoogle Scholar
Dubief, Y. & Delcayre, F. 2000 On coherent-vortex identification in turbulence. J. Turbul. 1, 1–22.CrossRefGoogle Scholar
Farge, M., Schneider, K. & Kevlahan, N. 1999 Non-Gaussianity and coherent vortex simulation for two-dimensional turbulence using an adaptive orthogonal wavelet basis. Phys. Fluids 11 (8), 2187–2201.CrossRefGoogle Scholar
Goldstein, D. E. & Vasilyev, O. V. 2004 Stochastic coherent adaptive large eddy simulation method. Phys. Fluids 16 (7), 2497–2513.CrossRefGoogle Scholar
Hunt, J. C. R., Wray, A. & Moin, P.1988 Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Report, CTR-S88.Google Scholar
Keetels, G. H., D’Ortona, U., Kramer, W., Clercs, H. J. H., Schneider, K. & van Heijst, G. J. F. 2007 Fourier spectral and wavelet solvers for the incompressible Navier–Stokes equations with volume-penalization: convergence of a dipole–wall collision. J. Comput. Phys. 227, 919–945.CrossRefGoogle Scholar
Kevlahan, N. K.-R., Alam, J. M. & Vasilyev, O. V. 2007 Scaling of space–time modes with Reynolds number in two-dimensional turbulence. J. Fluid Mech. 570, 217–226.CrossRefGoogle Scholar
Kevlahan, N. K.-R. & Vasilyev, O. V. 2005 An adaptive wavelet collocation method for fluid–structure interaction at high Reynolds numbers. SIAM J. Sci. Comput. 26 (6), 1894–1915.CrossRefGoogle Scholar
Luo, S. C., Chew, Y. T. & Ng, Y. T. 2003 Characteristics of square cylinder wake transition flows. Phys. Fluids 15 (9), 2549–2559.CrossRefGoogle Scholar
Lyn, D. A., Einav, S., Rodi, W. & Park, J. H. 1995 A laser-Doppler velocimetry study of ensemble-averaged characteristics of the turbulent flow near wake of a square cylinder. J. Fluid Mech. 304, 285–319.CrossRefGoogle Scholar
Lyn, D. A. & Rodi, W. 1994 The flapping shear layer formed by flow separation from the forward corner of a square cylinder. J. Fluid Mech. 267, 353–376.CrossRefGoogle Scholar
Nejadmalayeri, A. R.2012 Hierarchical multiscale adaptive variable fidelity wavelet-based turbulence modeling with lagrangian spatially variable thresholding. PhD thesis, University of Colorado Boulder, Boulder, CO.Google Scholar
Nejadmalayeri, A., Vezolainen, A. & Vasilyev, O. V. 2013 Reynolds number scaling of coherent vortex simulation and stochastic coherent adaptive large eddy simulation. Phys. Fluids 25, 110823, 1–15; doi:10.1063/1.4825260.CrossRefGoogle Scholar
Okajima, A. 1982 Strouhal numbers of rectangular cylinders. J. Fluid Mech. 123, 379–398.CrossRefGoogle Scholar
Robichaux, J., Balachandar, S. & Vanka, S. P. 1999 Three-dimensional Floquet instability of the wake of square cylinder. Phys. Fluids 11, 560–578.CrossRefGoogle Scholar
Saha, A. K., Biswas, G. & Muralidhar, K. 2003 Three-dimensional study of flow past a square cylinder at low Reynolds numbers. Intl J. Heat Fluid Flow 24, 54–66.CrossRefGoogle Scholar
Saha, A. K., Muralidhar, K. & Biswas, G. 2000 Experimental study of flow past a square cylinder at high Reynolds numbers. Exp. Fluids 29, 553–563.CrossRefGoogle Scholar
Schneider, K. & Vasilyev, O. V. 2010 Wavelet methods in computational fluid dynamics. Annu. Rev. Fluid Mech. 42, 473–503.CrossRefGoogle Scholar
Sheard, G. J., Fitzgerald, M. J. & Ryan, K. 2009 Cylinders with square cross-section: wake instabilities with incidence angle variation. J. Fluid Mech. 630, 43–69.CrossRefGoogle Scholar
Sohankar, A., Norberg, C. & Davidson, L. 1999 Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers. Phys. Fluids 11, 288–306.CrossRefGoogle Scholar
Vasilyev, O. V. 2003 Solving multi-dimensional evolution problems with localized structures using second generation wavelets. Intl J. Comput. Fluid Dyn. 17 (2), 151–168; Special issue on High-Resolution Methods in Computational Fluid Dynamics.CrossRefGoogle Scholar
Vasilyev, O. V. & Bowman, C. 2000 Second generation wavelet collocation method for the solution of partial differential equations. J. Comput. Phys. 165, 660–693.CrossRefGoogle Scholar
Vasilyev, O. V., De Stefano, G., Goldstein, D. E. & Kevlahan, N. K.-R. 2008 Lagrangian dynamic SGS model for stochastic coherent adaptive large eddy simulation. J. Turbul. 9 (11), 1–14.CrossRefGoogle Scholar
Vasilyev, O. V., Lund, T. S. & Moin, P. 1998 A general class of commutative filters for LES in complex geometries. J. Comput. Phys. 146, 105–123.CrossRefGoogle Scholar
Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539.CrossRefGoogle Scholar