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Properties Of The Cascaded Lattice Boltzmann Automaton

Author

Listed:
  • MARTIN GEIER

    (Lab for Simulation, Department of Microsystems Engineering (IMTEK), University of Freiburg, Georges-Köhler-Allee 103, 79110 Freiburg, Germany)

  • ANDREAS GREINER

    (Lab for Simulation, Department of Microsystems Engineering (IMTEK), University of Freiburg, Georges-Köhler-Allee 103, 79110 Freiburg, Germany)

  • JAN G. KORVINK

    (Lab for Simulation, Department of Microsystems Engineering (IMTEK), University of Freiburg, Georges-Köhler-Allee 103, 79110 Freiburg, Germany)

Abstract

The theory of the lattice Boltzmann automaton is based on a moment transform which is not Galilean invariant. It is explained how the central moments transform, used in the cascaded lattice Boltzmann method, overcomes this problem by choosing the center of mass coordinate system as the frame of reference. Galilean invariance is restored and the form of the kinetic theory is unaffected. Conservation laws are not compromised by the high order polyinomials in the equilibrium distribution arising from the central moment transform.Two sources of instabilities in lattice Boltzmann simulations are discussed: negative numerical viscosity due to insufficient Galilean invariance and aliasing. The cascaded lattice Boltzmann automaton overcomes both problems. It is discussed why aliasing is unavoidable in lattice Boltzmann methods that rely on a single relaxation time. An appendix lists the complete scattering operator of the D2Q9 cascaded lattice Boltzmann automaton.

Suggested Citation

  • Martin Geier & Andreas Greiner & Jan G. Korvink, 2007. "Properties Of The Cascaded Lattice Boltzmann Automaton," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 455-462.
    • Handle: RePEc:wsi:ijmpcx:v:18:y:2007:i:04:n:s0129183107010681
    DOI: 10.1142/S0129183107010681
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