Skip to main content
SpringerLink
Log in
Book cover

Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems pp 883–890Cite as

Towards a Stochastic Closure Approach for Large Eddy Simulation

  • Conference paper
  • First Online:

  • 1377 Accesses

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 78))

Abstract

We present a stochastic sub grid scale modeling strategy currently under development for application in Finite Volume Large Eddy Simulation (LES) codes. Our concept is based on the integral conservation laws for mass, momentum and energy of a flow field that are universally valid for arbitrary control volumes. We model the space-time structure of the fluxes to create a discrete formulation. Advanced methods of time series analysis for the data-based construction of stochastic models with inherently non-stationary statistical properties and concepts of information theory for the model discrimination are used to construct stochastic surrogate models for the non-resolved fluctuations. Vector-valued auto-regressive models with external influences (VARX-models) form the basis for the modeling approach. The reconstruction capabilities of the modeling ansatz are tested against fully three dimensional turbulent channel flow data computed by direct numerical simulation (DNS). We present here the outcome of our reconstruction tests.

Dr. P. Metzner was formerly associated with the University of Lugano, Switzerland.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Gassner, G.J., Beck, A.D.: On the accuracy of high-order discretizations for underresolved turbulence simulations. Theoret. Comput. Fluid Dyn. 27(3–4), 221–237 (2013). doi:10.1007/s00162-011-0253-7, http://dx.doi.org/10.1007/s00162-011-0253-7

  2. Hickel, S., Adams, N., Domaradzki, J.: And adaptive local deconvolution method for implicit les. J. Comput. Phys. 213, 413–436 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Jimenez, J., Moin, P.: The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240 (1991)

    Article  MATH  Google Scholar 

  4. Kim, J., Moin, P., Moser, R.: Turbulence statistics in fully developed channel flow at low reynolds number. J. Fluid Mech. 177, 133–166 (1987)

    Article  MATH  Google Scholar 

  5. von Larcher, T., Beck, A., Klein, R., Horenko, I., Metzner, P., Waidmann, M., Igdalov, D., Gassner, G., Munz, C.D.: A framework for the stochastic modelling of subgrid scale fluxes for large eddy simulation. Meteorol. Z. (Submitted)

    Google Scholar 

  6. van Leer, B.: Towards the ultimate conservative difference scheme. ii. monotonicity and conservation combined in a second-order scheme. J. Comput. Phys. 14, 361–370 (1974)

    Article  MATH  Google Scholar 

  7. Metzner, P., Putzig, L., Horenko, I.: Analysis of persistent non-stationary time series and applications. CAMCoS 7, 175–229 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  8. Moser, R., Kim, J., Mansour, N.: Direct numerical simulation of turbulent channel flow up to \({Re}_\tau =590\). Phys. Fluids 11(4), 943–945 (1999)

    Article  MATH  Google Scholar 

  9. Sagaut, P.: Large Eddy Simulation for Incompressible Flows. Springer, Berlin (2006)

    MATH  Google Scholar 

  10. Scotti, A., Meneveau, C.: A fractal model for large eddy simulation of turbulent flows. Physica D 127, 198–232 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  11. Shu, C.W.: Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. Technical Report 97–65, ICASE, NASA Langley Research Center, Hampton, VA (1997)

    Google Scholar 

  12. Uhlmann, M.: Generation of initial fields for channel flow investigation. Intermediate Report (2000). http://www-turbul.ifh.uni-karlsruhe.de/uhlmann/home/report.html. Accessed 15 Jan 2014

  13. Uhlmann, M.: The need for de-aliasing in a Chebyshev pseudo-spectral method. Technical Note No. 60 (2000). http://www-turbul.ifh.uni-karlsruhe.de/uhlmann/reports/dealias.pdf. Accessed 15th Jan 2014

Download references

Acknowledgments

The turbulent channel flow data were generated in the early 2000s in an extended DNS study by Markus Uhlmann at the Potsdam-Institute for Climate Impact Research within DFG-Project KL 611/10 using resources of the North-German Supercomputing Alliance (HLRN). Markus Uhlmann is now Professor at the Institute for Hydromechanics, Karlsruhe Institute of Technology, Germany. The processing of the channel flow data has been performed at HLRN, too. The study presented here has been funded by DFG, ref. no. KL 611/21.

Author information

Authors and Affiliations

  1. Institute of Mathematics, Freie Universität Berlin, Berlin, Germany

    Th. von Larcher, R. Klein & M. Waidmann

  2. Institute of Computational Science, Universita della Swizzerà italiana, Lugano, Switzerland

    I. Horenko, P. Metzner & D. Igdalov

  3. Institute of Aerodynamics and Gas Dynamics, University of Stuttgart, Stuttgart, Germany

    A. D. Beck & C. D. Munz

  4. Mathematical Institute, University of Cologne, Cologne, Germany

    G. J. Gassner

Authors
  1. Th. von Larcher
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Klein
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. Horenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. Metzner
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. Waidmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. D. Igdalov
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. A. D. Beck
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. G. J. Gassner
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. C. D. Munz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Th. von Larcher .

Editor information

Editors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany

    Jürgen Fuhrmann

  2. Institute Comp. Applied Mathematics, University of Münster Center for Nonlinear Sciences (CeNoS ), Münster, Germany

    Mario Ohlberger

  3. Inst. Appl. Analysis and Num. Simulation, University of Stuttgart, Stuttgart, Germany

    Christian Rohde

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Larcher, T.v. et al. (2014). Towards a Stochastic Closure Approach for Large Eddy Simulation. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems. Springer Proceedings in Mathematics & Statistics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-05591-6_89

Download citation

Publish with us

Policies and ethics

Search

Navigation