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Fully adaptive turbulence simulations based on Lagrangian spatio-temporally varying wavelet thresholding

Published online by Cambridge University Press:  22 May 2014

Alireza Nejadmalayeri ,
Alexei Vezolainen ,
Giuliano De Stefano  and
Oleg V. Vasilyev
Alireza Nejadmalayeri
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309, USA
Alexei Vezolainen
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309, USA
Giuliano De Stefano
Affiliation:
Dipartimento di Ingegneria Industriale e dell’Informazione, Seconda Università di Napoli, Aversa I-81031, Italy
Oleg V. Vasilyev*
Affiliation:
Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309, USA
*
†Email address for correspondence: [email protected]
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Abstract

A new framework for spatio-temporally adaptive turbulence simulations is proposed. The method is based on a variable-fidelity representation that tightly integrates numerics and modelling of subgrid-scale turbulence and aims to capture the flow physics on a near-optimal adaptive mesh. The integration is achieved by combining hierarchical wavelet-based computational modelling with spatially and temporally varying wavelet threshold filtering. The proposed approach provides automatic smooth transition from directly resolving all flow physics to capturing only the energetic/coherent structures, which leads to a dynamically adaptive variable-fidelity approach. The self-regulating continuous switch between different fidelity regimes is accomplished through a two-way feedback mechanism between the modelled dissipation and the local grid resolution, which is based on spatio-temporal variation of the wavelet filtering threshold. The proposed methodology systematically accounts for and exploits the spatial and temporal intermittency of turbulence. Thus, it overcomes the major limitation of all existing wavelet-based multi-resolution techniques, namely, the use of a global thresholding criterion. The procedure consists of tracking the wavelet thresholding factor within a Lagrangian frame by exploiting a Lagrangian path-line diffusive averaging approach, based on either interpolation along characteristics or direct solution of the corresponding evolution equation. This new methodology is tested for linearly forced homogeneous turbulence at different Reynolds numbers and provides very promising results on a benchmark with time-varying prescribed level of turbulence resolution.

JFM classification

Mathematical Foundations: Computational methods Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 749 , 25 June 2014 , pp. 794 - 817
Copyright
© 2014 Cambridge University Press 

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References

Chaouat, B. & Schiestel, R. 2005 A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows. Phys. Fluids 17 (6), 065106.1–065106.19; http://dx.doi.org/10.1063/1.1928607.Google Scholar
Daubechies, I. 1992 Ten Lectures on Wavelets, CBMS-NSF Series in Applied Mathematics, vol. 61. SIAM.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. 2013 Wavelet-based adaptive large-eddy simulation with explicit filtering. J. Comput. Phys. 238, 240–254.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, 045102.CrossRefGoogle Scholar
Farge, M. & Rabreau, G. 1988 Transformee en ondelettes pour detecter et analyser les structures coherentes dans les ecoulements turbulents bidimensionnels. C. R. Acad. Sci. Paris II 307, 1479–1486.Google Scholar
Farge, M. & Schneider, K. 2001 Coherent vortex simulation (CVS), a semi-deterministic turbulence model using wavelets. Flow Turbul. Combust. 6, 393–426.CrossRefGoogle Scholar
Farge, M., Schneider, K. & Kevlahan, N. K.-R. 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
Fröhlich, J. & Schneider, K. 1996 Numerical simulation of decaying turbulence in an adaptive wavelet basis. Appl. Comput. Harmon. Anal. 3, 393–397.CrossRefGoogle Scholar
Ghosal, S., Lund, T. S., Moin, P. & Akselvoll, K. 1995 A dynamic localization model for large-eddy simulation of turbulent flows. J. Fluid Mech. 286, 229–255.CrossRefGoogle Scholar
Girimaji, S. S. & Wallin, S. 2013 Closure modelling in bridging regions of variable-resolution (VR) turbulence computations. J. Turbul. 14 (1), 72–98.CrossRefGoogle Scholar
Goldstein, D. E. & Vasilyev, O. V. 2004 Stochastic coherent adaptive large eddy simulation method. Phys. Fluids 16 (7), 2497–2513.CrossRefGoogle Scholar
Goldstein, D. E., Vasilyev, O. V. & Kevlahan, N. K.-R. 2005 CVS and SCALES simulation of 3D isotropic turbulence. J. Turbul. 6 (37), 1–20.CrossRefGoogle Scholar
Jameson, L. 1998 A wavelet-optimized, very high order adaptive grid and order numerical method. SIAM J. Sci. Comput. 19 (6), 1980–2013.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
Liu, Q. & Vasilyev, O. V.2006 Hybrid adaptive wavelet collocation-brinkman penalization method for DNS and URANS simulations of compressible flow around bluff bodies. AIAA Paper 2006-3206.CrossRefGoogle Scholar
Lundgren, T. S.2003 Linearly forced isotropic turbulence. Annu. Res. Briefs, pp. 461–473. Center for Turbulence Research, Stanford University.Google Scholar
Meneveau, C., Lund, T. S. & Cabot, W. H. 1996 A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319, 353–385.CrossRefGoogle Scholar
Nejadmalayeri, A.2012 Hierarchical multiscale adaptive variable fidelity wavelet-based turbulence modelling with Lagrangian spatially variable thresholding. PhD thesis, University of Colorado Boulder, Boulder, CO.Google Scholar
Nejadmalayeri, A., Vasilyev, O. V., Vezolainen, A. & De Stefano, G. 2011 Spatially variable thresholding for stochastic coherent adaptive LES. In Proceedings of Direct and Large-Eddy Simulation Workshop 8: Eindhoven University of Technology, the Netherlands, July 7–9, 2010 (ed. Kuerten, H., Geurts, B., Armenio, V. & Fröhlich, J.), pp. 95–100. Springer.Google Scholar
Rosales, C. & Meneveau, C. 2005 Linear forcing in numerical simulations of isotropic turbulence: physical space implementations and convergence properties. Phys. Fluids 17, 1–8.CrossRefGoogle Scholar
Schiestel, R. & Dejoan, A. 2005 Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations. Theor. Comput. Fluid Dyn. 18 (6), 443–468.CrossRefGoogle Scholar
Schneider, K. & Vasilyev, O. V. 2010 Wavelet methods in computational fluid dynamics. Annu. Rev. Fluid Mech. 42, 473–503.CrossRefGoogle Scholar
Sweldens, W. 1996 The lifting scheme: a custom-design construction of biorthogonal wavelets. Appl. Comput. Harmon. Anal. 3 (2), 186–200.CrossRefGoogle Scholar
Vasilyev, O. V., De Stefano, G., Goldstein, D. E. & Kevlahan, N. K.-R. 2008 Lagrangian dynamic SGS model for SCALES of isotropic turbulence. J. Turbul. 9 (11), 1–14.Google Scholar