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Nonequilibrium entropy limiters in lattice Boltzmann methods

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  • Brownlee, R.A.
  • Gorban, A.N.
  • Levesley, J.

Abstract

We construct a system of nonequilibrium entropy limiters for the lattice Boltzmann methods (LBM). These limiters erase spurious oscillations without blurring of shocks, and do not affect smooth solutions. In general, they do the same work for LBM as flux limiters do for finite differences, finite volumes and finite elements methods, but for LBM the main idea behind the construction of nonequilibrium entropy limiter schemes is to transform a field of a scalar quantity — nonequilibrium entropy. There are two families of limiters: (i) based on restriction of nonequilibrium entropy (entropy “trimming”) and (ii) based on filtering of nonequilibrium entropy (entropy filtering). The physical properties of LBM provide some additional benefits: the control of entropy production and accurate estimation of introduced artificial dissipation are possible. The constructed limiters are tested on classical numerical examples: 1D athermal shock tubes with an initial density ratio 1:2 and the 2D lid-driven cavity for Reynolds numbers Re between 2000 and 7500 on a coarse 100×100 grid. All limiter constructions are applicable both for entropic and for non-entropic equilibria.

Suggested Citation

  • Brownlee, R.A. & Gorban, A.N. & Levesley, J., 2008. "Nonequilibrium entropy limiters in lattice Boltzmann methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 385-406.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:2:p:385-406
    DOI: 10.1016/j.physa.2007.09.031
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    References listed on IDEAS

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    1. Beck, Christian, 2006. "Stretched exponentials from superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 96-101.
    2. Tosi, F. & Ubertini, S. & Succi, S. & Chen, H. & Karlin, I.V., 2006. "Numerical stability of Entropic versus positivity-enforcing Lattice Boltzmann schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 72(2), pages 227-231.
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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.
    2. Bettaibi, Soufiene & Kuznik, Frédéric & Sediki, Ezeddine, 2016. "Hybrid LBM-MRT model coupled with finite difference method for double-diffusive mixed convection in rectangular enclosure with insulated moving lid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 311-326.
    3. Machado, Raúl, 2012. "On pressure and corner boundary conditions with two lattice Boltzmann construction approaches," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 84(C), pages 26-41.

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