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Non-hydrodynamic modes and general equations of state in lattice Boltzmann equations

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  • Dellar, Paul J.

Abstract

The lattice Boltzmann equation is commonly used to simulate fluids with isothermal equations of state in a weakly compressible limit, and intended to approximate solutions of the incompressible Navier–Stokes equations. Due to symmetry requirements there are usually more degrees of freedom in the equilibrium distributions than there are constraints imposed by the need to recover the Navier–Stokes equations in a slowly varying limit. We construct equilibria for general barotropic fluids, where pressure depends only upon density, using the two-dimensional, nine velocity (D2Q9) and one-dimensional, five velocity (D1Q5) lattices, showing that one otherwise arbitrary function in the equilibria must be chosen to suppress instability.

Suggested Citation

  • Dellar, Paul J., 2006. "Non-hydrodynamic modes and general equations of state in lattice Boltzmann equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(1), pages 132-138.
    • Handle: RePEc:eee:phsmap:v:362:y:2006:i:1:p:132-138
    DOI: 10.1016/j.physa.2005.09.012
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    Cited by:

    1. Gorban, A.N. & Packwood, D.J., 2014. "Enhancement of the stability of lattice Boltzmann methods by dissipation control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 285-299.

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