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Enhancement of the stability of lattice Boltzmann methods by dissipation control

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  • Gorban, A.N.
  • Packwood, D.J.

Abstract

Artificial dissipation is a well known tool for the improvement of stability of numerical algorithms. However, the use of this technique affects the accuracy of the computation. We analyse various approaches proposed for enhancement of the Lattice Boltzmann Methods’ (LBM) stability. In addition to some previously known methods, the Multiple Relaxation Time (MRT) models, the entropic lattice Boltzmann method (ELBM), and filtering (including entropic median filtering), we develop and analyse new filtering techniques with independent filtering of different modes. All these methods affect dissipation in the system and may adversely affect the reproduction of the proper physics. To analyse the effect of dissipation on accuracy and to prepare practical recommendations, we test the enhanced LBM methods on the standard benchmark, the 2D lid driven cavity on a coarse grid (101×101 nodes). The accuracy was estimated by the position of the first Hopf bifurcation points in these systems. We find that two techniques, MRT and median filtering, succeed in yielding a reasonable value of the Reynolds number for the first bifurcation point. The newly created limiters, which filter the modes independently, also pick a reasonable value of the Reynolds number for the first bifurcation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:414:y:2014:i:c:p:285-299
    DOI: 10.1016/j.physa.2014.07.052
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    References listed on IDEAS

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    1. Lätt, Jonas & Chopard, Bastien & Succi, Sauro & Toschi, Federico, 2006. "Numerical analysis of the averaged flow field in a turbulent lattice Boltzmann simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(1), pages 6-10.
    2. 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.
    3. 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.
    4. 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.
    5. Karlin, Iliya V. & Tatarinova, Larisa L. & Gorban, Alexander N. & Öttinger, Hans Christian, 2003. "Irreversibility in the short memory approximation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 327(3), pages 399-424.
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    Cited by:

    1. Oleg Ilyin, 2022. "Low Dissipative Entropic Lattice Boltzmann Method," Mathematics, MDPI, vol. 10(21), pages 1-22, October.
    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. Garcia, Salvador, 2017. "Chaos in the lid-driven square cavity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 142(C), pages 98-112.

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