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Non-dimensionalisation and Choice of Simulation Parameters

  • Timm Krüger
  • Halim Kusumaatmaja
  • Alexandr Kuzmin
  • Orest Shardt
  • Goncalo Silva
  • Erlend Magnus Viggen
Chapter
Part of the Graduate Texts in Physics book series (GTP)

Abstract

After reading this chapter, you will be familiar with how the “lattice units” usually used in simulations and articles can be related to physical units through unit conversion or through dimensionless numbers such as the Reynolds number. Additionally, you will be able to make good choices of simulation parameters and simulation resolution. As these are aspects of the lattice Boltzmann method that many beginners find puzzling, care is taken in this chapter to include a number of illustrative examples.

Keywords

Reynolds Number Mach Number Conversion Factor Poiseuille Flow Bond Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    E. Buckingham, Phys. Rev. 4, 345 (1914)ADSCrossRefGoogle Scholar
  2. 2.
    L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Pergamon Press, Oxford, 1987)zbMATHGoogle Scholar
  3. 3.
    E.M. Viggen, Phys. Rev. E 90, 013310 (2014)ADSCrossRefGoogle Scholar
  4. 4.
    Y.T. Feng, K. Han, D.R.J. Owen, Int. J. Numer. Meth. Eng. 72 (9), 1111–1134 (2007)MathSciNetCrossRefGoogle Scholar
  5. 5.
    P.A. Skordos, Phys. Rev. E 48 (6), 4823 (1993)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    D.J. Holdych, D.R. Noble, J.G. Georgiadis, R.O. Buckius, J. Comput. Phys. 193 (2), 595 (2004)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    S. Ubertini, P. Asinari, S. Succi, Phys. Rev. E 81 (1), 016311 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    P.J. Dellar, Comput. Math. Appl. 65 (2), 129 (2013)MathSciNetCrossRefGoogle Scholar
  9. 9.
    M. Reider, J. Sterling, Comput. Fluids 118, 459 (1995)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    D. d’Humières, I. Ginzburg, Comput. Math. Appl. 58, 823 (2009)MathSciNetCrossRefGoogle Scholar
  11. 11.
    T. Krüger, F. Varnik, D. Raabe, Phys. Rev. E 79 (4), 046704 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    I. Ginzburg, D. d’Humières, A. Kuzmin, J. Stat. Phys. 139, 1090 (2010)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    J.C.G. Verschaeve, Phys. Rev. E 80, 036703 (2009)ADSCrossRefGoogle Scholar
  14. 14.
    A. Kuzmin, M. Januszewski, D. Eskin, F. Mostowfi, J. Derksen, Chem. Eng. J. 171, 646 (2011)CrossRefGoogle Scholar
  15. 15.
    A. Kuzmin, M. Januszewski, D. Eskin, F. Mostowfi, J. Derksen, Chem. Eng. J. 178, 306 (2011)CrossRefGoogle Scholar
  16. 16.
    T. Krüger, D. Holmes, P.V. Coveney, Biomicrofluidics 8 (5), 054114 (2014)CrossRefGoogle Scholar
  17. 17.
    M.E. Cates, J.C. Desplat, P. Stansell, A.J. Wagner, K. Stratford, R. Adhikari, I. Pagonabarraga, Philos. T. Roy. Soc. A 363 (1833), 1917 (2005)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Oxford University Press, Oxford, 2001)zbMATHGoogle Scholar
  19. 19.
    X. He, G. Doolen, J. Comput. Phys. 134, 306 (1997)ADSCrossRefGoogle Scholar
  20. 20.
    A.M.M. Artoli, A.G. Hoekstra, P.M.A. Sloot, Comput. Fluids 35 (2), 227 (2006)CrossRefGoogle Scholar
  21. 21.
    R.W. Nash, H.B. Carver, M.O. Bernabeu, J. Hetherington, D. Groen, T. Krüger, P.V. Coveney, Phys. Rev. E 89 (2), 023303 (2014)ADSCrossRefGoogle Scholar
  22. 22.
    B. Dünweg, A.J.C. Ladd, in Advances in Polymer Science (Springer, Berlin, Heidelberg, 2008), pp. 1–78Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Timm Krüger
    • 1
  • Halim Kusumaatmaja
    • 2
  • Alexandr Kuzmin
    • 3
  • Orest Shardt
    • 4
  • Goncalo Silva
    • 5
  • Erlend Magnus Viggen
    • 6
  1. 1.School of Engineering University of EdinburghEdinburghUK
  2. 2.Department of PhysicsDurham UniversityDurhamUK
  3. 3.Maya Heat Transfer TechnologiesWestmountCanada
  4. 4.Department of Mechanical and Aerospace EngineeringPrinceton UniversityPrincetonUSA
  5. 5.IDMEC/IST, University of LisbonLisbonPortugal
  6. 6.Acoustics Research Centre, SINTEF ICTTrondheimNorway

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