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Wavelet-based adaptive large-eddy simulation of supersonic channel flow

Published online by Cambridge University Press:  25 August 2020

Giuliano De Stefano Open the ORCID record for Giuliano De Stefano [Opens in a new window] ,
Eric Brown-Dymkoski  and
Oleg V. Vasilyev Open the ORCID record for Oleg V. Vasilyev [Opens in a new window]
Giuliano De Stefano*
Affiliation:
Department of Engineering, University of Campania, Aversa, I-81031, Italy
Eric Brown-Dymkoski
Affiliation:
Space Exploration Technologies Corp. (SpaceX), Hawthorne, CA90250, USA
Oleg V. Vasilyev*
Affiliation:
Adaptive Wavelet Technologies, LLC, Superior, CO80027, USA Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, 125047, Russia
*
†Email addresses for correspondence: giuliano.destefano@unicampania.it, oleg.v.vasilyev@adaptivewavelettechnologies.com, oleg.v.vasilyev@gmail.com
†Email addresses for correspondence: giuliano.destefano@unicampania.it, oleg.v.vasilyev@adaptivewavelettechnologies.com, oleg.v.vasilyev@gmail.com
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Abstract

The wavelet-based adaptive large-eddy simulation method is extended for computational modelling of compressible wall-bounded attached turbulent flows. The wavelet-threshold filtered compressible Navier–Stokes equations are derived. The unclosed terms in the governing equations are approximated by using eddy-viscosity and eddy-conductivity modelling procedures based on the anisotropic minimum-dissipation approach. The proposed filtering procedure is integrated with the adaptive anisotropic wavelet collocation method, which allows for the appropriate mesh stretching in the wall-normal direction. The performance of the method is assessed by conducting adaptive numerical simulations of fully developed supersonic flow in a plane channel with isothermal walls, which represents a well-established benchmark for wall-bounded turbulent compressible flows. The present results demonstrate both the feasibility and the effectiveness of the novel wavelet-based adaptive method in the high-speed compressible regime, showing good agreement with reference numerical solutions.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , A13
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Abkar, M., Bae, H. J. & Moin, P. 2016 Minimum-dissipation scalar transport model for large-eddy simulation of turbulent flows. Phys. Rev. Fluids 1, 041701.CrossRefGoogle Scholar
Brown-Dymkoski, E. & Vasilyev, O. V. 2017 Adaptive-anisotropic wavelet collocation method on general curvilinear coordinate systems. J. Comput. Phys. 333, 414–426.CrossRefGoogle Scholar
Brun, C., Petrovan Boiarciuc, M., Haberkorn, M. & Comte, P. 2008 Large eddy simulation of compressible channel flow. Theor. Comput. Fluid Dyn. 22, 189–212.CrossRefGoogle Scholar
Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4 (8), 1637–1650.CrossRefGoogle Scholar
Coleman, G. N., Kim, J. & Moser, R. D. 1995 A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305, 159–183.CrossRefGoogle Scholar
Courant, R., Friedrichs, K. & Lewy, H. 1928 Über die partiellen differenzengleichungen der mathematischen physik. Math. Ann. 100, 32–74.CrossRefGoogle Scholar
De Stefano, G., Goldstein, D. E. & Vasilyev, O. V. 2005 On the role of subgrid-scale coherent modes in large-eddy simulation. J. Fluid Mech. 525, 263–274.CrossRefGoogle Scholar
De Stefano, G., Nejadmalayeri, A. & Vasilyev, O. V. 2016 Wall-resolved wavelet-based adaptive large-eddy simulation of bluff-body flows with variable thresholding. J. Fluid Mech. 788, 303–336.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. 2014 Wavelet-based adaptive simulations of three-dimensional flow past a square cylinder. J. Fluid Mech. 748, 433–456.CrossRefGoogle Scholar
De Stefano, G., Vasilyev, O. V. & Brown-Dymkoski, E. 2018 Wavelet-based adaptive unsteady Reynolds-averaged turbulence modelling of external flows. J. Fluid Mech. 837, 765–787.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.CrossRefGoogle Scholar
Donoho, D. L. 1992 Interpolating wavelet transforms. Tech Rep. 3. Department of Statistics, Stanford University.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 1760–1765.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 3-d isotropic turbulence. J. Turbul. 6 (37), 1–20.CrossRefGoogle Scholar
Huang, P. G., Coleman, G. N. & Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modeling. J. Fluid Mech. 305, 185–218.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
Lechner, R., Sesterhenn, J. & Friedrich, R. 2001 Turbulent supersonic channel flow. J. Turbul. 2, 1–25.CrossRefGoogle Scholar
Lenormand, E., Sagaut, P. & Ta Phuoc, L. 2000 a Large eddy simulation of subsonic and supersonic channel flow at moderate Reynolds number. Intl J. Numer. Meth. Fluids 32, 369–406.3.0.CO;2-6>CrossRefGoogle Scholar
Lenormand, E., Sagaut, P., Ta Phuoc, L. & Comte, P. 2000 b Subgrid-scale models for large-eddy simulations of compressible wall bounded flows. AIAA J. 38 (8), 1340–1350.CrossRefGoogle Scholar
Lesieur, M., Métais, O. & Comte, P. 2005 Large-Eddy Simulations of Turbulence. Cambridge University Press.CrossRefGoogle Scholar
Martín, M. P., Piomelli, U. & Candler, G. V. 2000 Subgrid-scale models for compressible large-eddy simulations. Theor. Comput. Fluid Dyn. 13, 361–376.Google Scholar
Modesti, D. & Pirozzoli, S. 2016 Reynolds and Mach number effects in compressible turbulent channel flow. Intl J. Heat Fluid Flow 59, 33–49.CrossRefGoogle Scholar
Moin, P., Squires, K., Cabot, W. & Lee, S. 1991 A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids A 3, 2746–2757.CrossRefGoogle Scholar
Morinishi, Y., Tamano, S. & Nakabayashi, K. 2004 Direct numerical simulation of compressible turbulent channel flow between adiabatic and isothermal walls. J. Fluid Mech. 502, 273–308.CrossRefGoogle Scholar
Nejadmalayeri, A., Vezolainen, A., Brown-Dymkoski, E. & Vasilyev, O. V. 2015 Parallel adaptive wavelet collocation method for PDEs. J. Comput. Phys. 298, 237–253.CrossRefGoogle Scholar
Nejadmalayeri, A., Vezolainen, A., De Stefano, G. & Vasilyev, O. V. 2014 Fully adaptive turbulence simulations based on Lagrangian spatio-temporally varying wavelet thresholding. J. Fluid Mech. 749, 794–817.CrossRefGoogle 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.CrossRefGoogle Scholar
Paolucci, S., Zikoski, Z. J. & Wirasaet, D. 2014 WAMR: an adaptive wavelet method for the simulation of compressible reacting flow. Part I. Accuracy and efficiency of algorithm. J. Comput. Phys. 272, 814–841.CrossRefGoogle Scholar
Roussel, O. & Schneider, K. 2010 Coherent vortex simulation of weakly compressible turbulent mixing layers using adaptive multiresolution methods. J. Comput. Phys. 229 (6), 2267–2286.CrossRefGoogle Scholar
Rozema, W., Bae, H. J., Moin, P. & Verstappen, R. 2015 Minimum-dissipation models for large-eddy simulation. Phys. Fluids 27 (8), 085107.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. 1998 The lifting scheme: a construction of second generation wavelets. SIAM J. Math. Anal. 29 (2), 511–546.CrossRefGoogle Scholar
Vasilyev, O. V. 2003 Solving multi-dimensional evolution problems with localized structures using second generation wavelets. Intl J. Comput. Fluid Dyn. 17, 151–168.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, 1–11.CrossRefGoogle Scholar
Vasilyev, O. V., Yuen, D. A. & Paolucci, S. 1997 The solution of PDEs using wavelets. Comput. Phys. 11 (5), 429–435.CrossRefGoogle Scholar
Verstappen, R. 2011 When does eddy viscosity damp subfilter scales sufficiently? J. Sci. Comput. 49 (1), 94–110.CrossRefGoogle Scholar
Vreman, B., Geurts, B. & Kuerten, H. 1995 A priori tests of large eddy simulation of compressible plane mixing layer. J. Engng Maths 29, 299–327.CrossRefGoogle Scholar
Vreman, B., Geurts, B. & Kuerten, H. 1997 Large-eddy simulation of the turbulent mixing layer. J. Fluid Mech. 339, 357–390.CrossRefGoogle Scholar