Advertisement

The European Physical Journal Special Topics

, Volume 223, Issue 11, pp 2177–2188 | Cite as

Relativistic lattice kinetic theory: Recent developments and future prospects

  • S. Succi
  • M. Mendoza
  • F. Mohseni
  • I. Karlin
Review
Part of the following topical collections:
  1. Dynamic Systems: From Statistical Mechanics to Engineering Applications

Abstract

In this paper, we review recent progress in relativistic lattice kinetic theory and its applications to relativistic hydrodynamics. Two methods for constructing the discretised distribution function, moment matching and projection onto orthogonal polynomials, are described. Extensions to ultra-high velocities as well as improved dissipation models are discussed. We show that the existing models can successfully cover a wide range of velocities (from weak-relativistic to ultra-relativistic) and viscous regimes. Various applications, from quark-gluon plasma and relativistic Richtmyer-Meshkov instability to flows in curved manifolds are also explored. Finally, potential developments for general relativity are outlined along with future prospects for solving the full set of Einstein equations of general relativity.

Keywords

Shock Wave Boltzmann Equation European Physical Journal Special Topic Riemann Problem Relativistic Hydrodynamic 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Chen, S. Chen, W. Matthaeus, Phys. Rev. A 45, 5339 (1992)CrossRefADSGoogle Scholar
  2. 2.
    R. Benzi, S. Succi, M. Vergassola, Phys. Rep. 222, 145 (1992)CrossRefADSGoogle Scholar
  3. 3.
    S. Succi, The lattice Boltzmann Equation for Fluid Dynamics and Beyond (Oxford University Press, New York, 2001)Google Scholar
  4. 4.
    M. Mendoza, F. Wittel, H. Herrmann, Eur. Phys. J. E 32, 339 (2010)CrossRefGoogle Scholar
  5. 5.
    S. Succi, The Eur. Phys. J. B 64, 471 (2008)CrossRefADSGoogle Scholar
  6. 6.
    C.K. Aidun, J.R. Clausen, Annu. Rev. Fluid Mech. 42, 439 (2010)MathSciNetCrossRefADSGoogle Scholar
  7. 7.
    K. Novoselov, A. Geim, S. Morozov, D. Jiang, M. Katsnelson, I. Grigorieva, S. Dubonos, Nat. Lett. 438, 197 (2005)CrossRefADSGoogle Scholar
  8. 8.
    M. Müller, J. Schmalian, L. Fritz, Phys. Rev. Lett. 103, 025301 (2009)CrossRefADSGoogle Scholar
  9. 9.
    M. Mendoza, H. Herrmann, S. Succi, Sci. Rep. 3 (2013)Google Scholar
  10. 10.
    M. Mendoza, H. Herrmann, S. Succi, Phys. Rev. Lett. 106, 156601 (2011)CrossRefADSGoogle Scholar
  11. 11.
    E. Shuryak, Prog. Part. Nuc. Phys. 53, 273 (2004)CrossRefADSGoogle Scholar
  12. 12.
    P.K. Kovtun, D.T. Son, A.O. Starinets, Phys. Rev. Lett. 94, 111601 (2005)CrossRefADSGoogle Scholar
  13. 13.
    S. Siegler, H. Riffert, Astrophys. J. 531, 1053 (2008)CrossRefADSGoogle Scholar
  14. 14.
    M. Dubal, Comput. Phys. Commun. 64, 221 (1991)CrossRefADSGoogle Scholar
  15. 15.
    M. Mendoza, B. Boghosian, H. Herrmann, S. Succi, Phys. Rev. Lett. 105, 014502 (2010)CrossRefADSGoogle Scholar
  16. 16.
    C. Marle, C. Hebad, Seances Acad. Sci. 260, 6539 (1965)zbMATHGoogle Scholar
  17. 17.
    J. Anderson, H. Witting, Physica 74, 466 (1974)CrossRefADSGoogle Scholar
  18. 18.
    M. Mendoza, B.M. Boghosian, H.J. Herrmann, S. Succi, Phys. Rev. D 82(10), 105008 (2010)CrossRefADSGoogle Scholar
  19. 19.
    I. Bouras, E. Molnar, H. Niemi, Z. Xu, A. El, O. Fochler, C. Greiner, D.H. Rischke, Phys. Rev. Lett. 103, 032301 (2009)CrossRefADSGoogle Scholar
  20. 20.
    F. Mohseni, M. Mendoza, S. Succi, H.J. Herrmann, Phys. Rev. D 87, 083003 (2013)CrossRefADSGoogle Scholar
  21. 21.
    M. Mendoza, I. Karlin, S. Succi, H. Herrmann, Phys. Rev. D 87, 065027 (2013)CrossRefADSGoogle Scholar
  22. 22.
    Z. Xu, C. Greiner, H. Stöcker, Phys. Rev. Lett. 101, 082302 (2008)CrossRefADSGoogle Scholar
  23. 23.
    W. Scheid, H. Müller, W. Greiner, Phys. Rev. Lett. 32, 741 (1974)CrossRefADSGoogle Scholar
  24. 24.
    H.H. Gutbrod, K.H. Kampert, B. Kolb, A.M. Poskanzer, H.G. Ritter, R. Schicker, H.R. Schmidt, Phys. Rev. C 42, 640 (1990)CrossRefADSGoogle Scholar
  25. 25.
    V. Goncharov, Phys. Rev. Lett. 82, 2091 (1999)CrossRefADSGoogle Scholar
  26. 26.
    D. Arnett, Astrophys. J. Supp. Ser. 127, 213 (2000)CrossRefADSGoogle Scholar
  27. 27.
    M. Mendoza, S. Succi, H. Herrmann, Sci. Rep. 3 (2013)Google Scholar
  28. 28.
    E. Priest, Solar Magneto-hydrodynamics, Geophysics and astrophysics monographs (D. Reidel Pub. Co., 1984), ISBN: 9789027718334Google Scholar
  29. 29.
    S.S. Chikatamarla, I.V. Karlin, Phys. Rev. E 79, 046701 (2009)MathSciNetCrossRefADSGoogle Scholar
  30. 30.
    I. Karlin, D. Sichau, S. Chikatamarla, Phys. Rev. E 88, 063310 (2013)CrossRefADSGoogle Scholar
  31. 31.
    G. Yan, J. Zhang, Math. Comput. Simulat. 79, 1554 (2009)CrossRefzbMATHGoogle Scholar
  32. 32.
    J. Zhang, G. Yan, Physica A 387, 4771 (2008)MathSciNetCrossRefADSGoogle Scholar
  33. 33.
    S. Palpacelli, S. Succi, R. Spigler, Phys. Rev. E 76, 036712 (2007)CrossRefADSGoogle Scholar
  34. 34.
    S. Palpacelli, S. Succi, Phys. Rev. E 77, 066708 (2008)CrossRefADSGoogle Scholar
  35. 35.
    F. Pretorius, W. Israel, Classical Quant. Grav. 15, 2289 (1998)MathSciNetCrossRefzbMATHADSGoogle Scholar
  36. 36.
    F. Pretorius, Phys. Rev. Lett. 95, 121101 (2005)MathSciNetCrossRefADSGoogle Scholar
  37. 37.
    M. Ottaviani, F. Romanelli, R. Benzi, M. Briscolini, P. Santangelo, S. Succi, Phys. Fluids B 2, 67 (1990)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  • S. Succi
    • 3
  • M. Mendoza
    • 2
  • F. Mohseni
    • 2
  • I. Karlin
    • 1
  1. 1.ETH Zürich, Department of Mechanical and Process EngineeringZürichSwitzerland
  2. 2.ETH Zürich, Computational Physics for Engineering Materials, Institute for Building MaterialsZürichSwitzerland
  3. 3.Istituto per le Applicazioni del Calcolo C.N.R.RomeItaly

Personalised recommendations