Basics of Hydrodynamics and Kinetic Theory

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


After reading this chapter, you will have a working understanding of the equations of fluid mechanics, which describe a fluid’s behaviour through its conservation of mass and momentum. You will understand the basics of the kinetic theory on which the lattice Boltzmann method is founded. Additionally, you will have learned about how different descriptions of a fluid, such as the continuum fluid description and the mesoscopic kinetic description, are related.


Boltzmann Equation Kinetic Theory Knudsen Number Lattice Boltzmann Method Collision Operator 
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.


  1. 1.
    G.K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 2000)CrossRefzbMATHGoogle Scholar
  2. 2.
    P.A. Thompson, Compressible-Fluid Dynamics (McGraw-Hill, New York, 1972)zbMATHGoogle Scholar
  3. 3.
    L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Pergamon Press, Oxford, 1987)zbMATHGoogle Scholar
  4. 4.
    W.P. Graebel, Advanced Fluid Mechanics (Academic Press, Burlington, 2007)Google Scholar
  5. 5.
    L.E. Kinsler, A.R. Frey, A.B. Coppens, J.V. Sanders, Fundamentals of Acoustics, 4th edn. (Wiley, New York, 2000)Google Scholar
  6. 6.
    M. Born, H.S. Green, Proc. R. Soc. A 188 (1012), 10 (1946)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    C.S. Wang Chang, G. Uhlenbeck, Transport phenomena in polyatomic gases. Tech. Rep. M604-6, University of Michigan (1951)Google Scholar
  8. 8.
    S. Chapman, T.G. Cowling, The Mathematical Theory of Non-uniform Gases, 2nd edn. (Cambridge University Press, Cambridge, 1952)zbMATHGoogle Scholar
  9. 9.
    T.F. Morse, Phys. Fluids 7 (2), 159 (1964)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    C. Cercignani, The Boltzmann Equation and Its Applications (Springer, New York, 1988)CrossRefzbMATHGoogle Scholar
  11. 11.
    T.I. Gombosi, Gaskinetic Theory (Cambridge University Press, Cambridge, 1994)CrossRefGoogle Scholar
  12. 12.
    D. Hänel, Molekulare Gasdynamik (Springer, New York, 2004)Google Scholar
  13. 13.
    P.L. Bhatnagar, E.P. Gross, M. Krook, Phys. Rev. E 94 (3), 511 (1954)ADSCrossRefGoogle Scholar
  14. 14.
    E.M. Viggen, The lattice Boltzmann method: Fundamentals and acoustics. Ph.D. thesis, Norwegian University of Science and Technology (NTNU), Trondheim (2014)Google Scholar
  15. 15.
    M. Greenspan, in Physical Acoustics, vol. IIA, ed. by W.P. Mason (Academic Press, San Diego, 1965), pp. 1–45Google Scholar
  16. 16.
    E.T. Jaynes, Am. J. Phys. 33 (5), 391 (1965)ADSCrossRefGoogle 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

Personalised recommendations