Skip to main content
Top
Published in: Mathematical Models and Computer Simulations 3/2020

01-05-2020

Generation of Three-Dimensional Homogeneous Isotropic Turbulent Velocity Fields Using the Randomized Spectral Method

Authors: A. V. Alexandrov, L. W. Dorodnicyn, A. P. Duben

Published in: Mathematical Models and Computer Simulations | Issue 3/2020

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This work studies a stochastic method for the generation of artificial three-dimensional, divergence-free, homogeneous, and isotropic velocity fields. The technique is based on the randomized spectral method. The statistical and spectral properties of turbulent fields constructed by this generator are analyzed. A validation LES-based computation which uses the obtained turbulent fields as initial conditions, demonstrates good agreement of the results with the experimental data.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference R. Kraichnan, “Diffusion by a random velocity field,” Phys. Fluids 13 (1), 22–31 (1970).CrossRef R. Kraichnan, “Diffusion by a random velocity field,” Phys. Fluids 13 (1), 22–31 (1970).CrossRef
2.
go back to reference M. Karweit, Ph. Blanc-Benon, D. Juve, and G. Comte-Bellot, “Simulation of the propagation of an acoustic wave through a turbulent velocity field: a study of phase variance,” J. Acoust. Soc. Am. 89 (1) (1991). M. Karweit, Ph. Blanc-Benon, D. Juve, and G. Comte-Bellot, “Simulation of the propagation of an acoustic wave through a turbulent velocity field: a study of phase variance,” J. Acoust. Soc. Am. 89 (1) (1991).
3.
go back to reference W. Bechara, C. Bailly, P. Lafon, and S. M. Candel, “Stochastic approach to noise modeling for free turbulent flows,” AIAA J. 32, 455–463 (1994).CrossRef W. Bechara, C. Bailly, P. Lafon, and S. M. Candel, “Stochastic approach to noise modeling for free turbulent flows,” AIAA J. 32, 455–463 (1994).CrossRef
4.
go back to reference C. Bailly and D. Juve, “A stochastic approach to compute subsonic-noise using linearized Euler’s equations,” AIAA Paper No. 99-1872, A99-27849. C. Bailly and D. Juve, “A stochastic approach to compute subsonic-noise using linearized Euler’s equations,” AIAA Paper No. 99-1872, A99-27849.
5.
go back to reference I. A. Borovskaya, “Modeling of homogeneous random fields with specific spectrum for aeroacoustics problems,” Mat. Model. 19 (7), 67–76 (2007).MathSciNet I. A. Borovskaya, “Modeling of homogeneous random fields with specific spectrum for aeroacoustics problems,” Mat. Model. 19 (7), 67–76 (2007).MathSciNet
6.
go back to reference I. A. Borovskaya, T. K. Kozubskaya, O. Kurbanmuradov, and K. K. Sabelfeld, “On modeling of homogeneous random fields and signals and their applications in aeroacoustics problems,” Mat. Model. 19 (10), 76–88 (2007).MathSciNetMATH I. A. Borovskaya, T. K. Kozubskaya, O. Kurbanmuradov, and K. K. Sabelfeld, “On modeling of homogeneous random fields and signals and their applications in aeroacoustics problems,” Mat. Model. 19 (10), 76–88 (2007).MathSciNetMATH
7.
go back to reference T. Saad, D. Cline, R. Stoll, and J. C. Sutherland, “Scalable tools for generating synthetic isotropic turbulence with arbitrary spectra,” AIAA J. 55 (18), 327–331 (2016).CrossRef T. Saad, D. Cline, R. Stoll, and J. C. Sutherland, “Scalable tools for generating synthetic isotropic turbulence with arbitrary spectra,” AIAA J. 55 (18), 327–331 (2016).CrossRef
8.
go back to reference D. Yu. Adamyan, “A method for generating synthetic turbulence at the inflow boundaries for calculating turbulent flows in the framework of eddy-resolving approaches,” Cand. Sci. (Phys. Math.) Dissertation (St. Petersburg, 2011). D. Yu. Adamyan, “A method for generating synthetic turbulence at the inflow boundaries for calculating turbulent flows in the framework of eddy-resolving approaches,” Cand. Sci. (Phys. Math.) Dissertation (St. Petersburg, 2011).
10.
go back to reference N. S. Dhamankar, G. A. Blaisdell, and A. S. Lyrintzis, “Overview of turbulent inflow boundary conditions for Large-Eddy Simulations,” AIAA J. 56, 1317–1334 (2018).CrossRef N. S. Dhamankar, G. A. Blaisdell, and A. S. Lyrintzis, “Overview of turbulent inflow boundary conditions for Large-Eddy Simulations,” AIAA J. 56, 1317–1334 (2018).CrossRef
11.
go back to reference P. Batten, U. Goldberg, and S. Chakravarthy, “Interfacing statistical turbulence closures with Large-Eddy Simulation,” AIAA J. 42, 485–492 (2004).CrossRef P. Batten, U. Goldberg, and S. Chakravarthy, “Interfacing statistical turbulence closures with Large-Eddy Simulation,” AIAA J. 42, 485–492 (2004).CrossRef
12.
go back to reference A. Smirnov, S. Shi, and I. Celik, “Random flow generation technique for Large Eddy Simulations and particle-dynamics modeling,” J. Fluids Eng. 123, 359–371 (2001).CrossRef A. Smirnov, S. Shi, and I. Celik, “Random flow generation technique for Large Eddy Simulations and particle-dynamics modeling,” J. Fluids Eng. 123, 359–371 (2001).CrossRef
13.
go back to reference K. K. Sabelfeld, Monte Carlo Methods in Boundary Value Problems (Springer, Heidelberg, Berlin, New York, 1991). K. K. Sabelfeld, Monte Carlo Methods in Boundary Value Problems (Springer, Heidelberg, Berlin, New York, 1991).
14.
go back to reference O. Kurbanmuradov and K. Sabelfeld, “Stochastic spectral and Fourier-wavelet methods for vector Gaussian random fields,” Monte Carlo Methods Appl. 12, 395–445 (2006).MathSciNetCrossRef O. Kurbanmuradov and K. Sabelfeld, “Stochastic spectral and Fourier-wavelet methods for vector Gaussian random fields,” Monte Carlo Methods Appl. 12, 395–445 (2006).MathSciNetCrossRef
15.
go back to reference O. Kurbanmuradov, K. Sabelfeld, and P. R. Kramer, “Randomized spectral and Fourier-wavelet methods for multidimensional Gaussian random vector fields,” J. Comput. Phys. 245, 218–234 (2013).MathSciNetCrossRef O. Kurbanmuradov, K. Sabelfeld, and P. R. Kramer, “Randomized spectral and Fourier-wavelet methods for multidimensional Gaussian random vector fields,” J. Comput. Phys. 245, 218–234 (2013).MathSciNetCrossRef
16.
go back to reference G. Comte-Bellot and S. Corrsin, “Simple Eulerian time correlation of full- and narrow-band velocity signals in grid-generated 'isotropic' turbulence,” J. Fluid Mech. 48, 273–337 (1971).CrossRef G. Comte-Bellot and S. Corrsin, “Simple Eulerian time correlation of full- and narrow-band velocity signals in grid-generated 'isotropic' turbulence,” J. Fluid Mech. 48, 273–337 (1971).CrossRef
17.
go back to reference A. V. Aleksandrov, L. V. Dorodnitsyn, and A. P. Duben, “Generation of three-dimensional turbulent velocity fields on the base of a randomized spectral method,” KIAM Preprint No. 221 (Keldysh Inst. Appl. Math., Moscow, 2018). A. V. Aleksandrov, L. V. Dorodnitsyn, and A. P. Duben, “Generation of three-dimensional turbulent velocity fields on the base of a randomized spectral method,” KIAM Preprint No. 221 (Keldysh Inst. Appl. Math., Moscow, 2018).
18.
go back to reference J. O. Hinze, Turbulence: An Introduction to Its Mechanism and Theory, 2nd ed. (McGraw Hill, New York, 1959). J. O. Hinze, Turbulence: An Introduction to Its Mechanism and Theory, 2nd ed. (McGraw Hill, New York, 1959).
19.
go back to reference J. Smagorinsky, “General circulation experiments with the primitive equations. I. The basic experiment,” Month. Wea. Rev. 91, 99–164 (1963).CrossRef J. Smagorinsky, “General circulation experiments with the primitive equations. I. The basic experiment,” Month. Wea. Rev. 91, 99–164 (1963).CrossRef
20.
go back to reference I. V. Abalakin, P. A. Bakhvalov, A. V. Gorobets, A. P. Duben, and T. K. Kozubskaya, “Parallel research code NOISEtte for large-scale CFD and CAA simulations,” Vychisl. Metody Programm. 13 (3), 110–125 (2012). I. V. Abalakin, P. A. Bakhvalov, A. V. Gorobets, A. P. Duben, and T. K. Kozubskaya, “Parallel research code NOISEtte for large-scale CFD and CAA simulations,” Vychisl. Metody Programm. 13 (3), 110–125 (2012).
22.
go back to reference A. P. Duben, T. K. Kozubskaya, and D. V. Potapov, “Simulation of unsteady isotropic turbulent flows on unstructured meshes using edge-based algorithms,” Mat. Model. 29 (5), 27–45 (2017).MathSciNetMATH A. P. Duben, T. K. Kozubskaya, and D. V. Potapov, “Simulation of unsteady isotropic turbulent flows on unstructured meshes using edge-based algorithms,” Mat. Model. 29 (5), 27–45 (2017).MathSciNetMATH
Metadata
Title
Generation of Three-Dimensional Homogeneous Isotropic Turbulent Velocity Fields Using the Randomized Spectral Method
Authors
A. V. Alexandrov
L. W. Dorodnicyn
A. P. Duben
Publication date
01-05-2020
Publisher
Pleiades Publishing
Published in
Mathematical Models and Computer Simulations / Issue 3/2020
Print ISSN: 2070-0482
Electronic ISSN: 2070-0490
DOI
https://doi.org/10.1134/S2070048220030047

Other articles of this Issue 3/2020

Mathematical Models and Computer Simulations 3/2020 Go to the issue

Premium Partner