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Structural stability of Lattice Boltzmann schemes

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  • David, Claire
  • Sagaut, Pierre

Abstract

The goal of this work is to determine classes of traveling solitary wave solutions for Lattice Boltzmann schemes by means of a hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation. The occurrence of such a spurious solitary wave, which exhibits a very long life time, results in a non-vanishing numerical error for arbitrary time in unbounded numerical domain. Such a behavior is referred here to have a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasses types of solutions (solitary waves in the present case) that are not solutions of the original continuous equations. This paper extends our previous work about classical schemes to Lattice Boltzmann schemes (David and Sagaut 2011; 2009a,b; David et al. 2007).

Suggested Citation

  • David, Claire & Sagaut, Pierre, 2016. "Structural stability of Lattice Boltzmann schemes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 1-8.
    • Handle: RePEc:eee:phsmap:v:444:y:2016:i:c:p:1-8
    DOI: 10.1016/j.physa.2015.09.089
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    References listed on IDEAS

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    1. Bastien Chopard & Alexandre Dupuis & Alexandre Masselot & Pascal Luthi, 2002. "Cellular Automata And Lattice Boltzmann Techniques: An Approach To Model And Simulate Complex Systems," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 5(02n03), pages 103-246.
    2. Feng, Zhaosheng & Chen, Goong, 2005. "Solitary wave solutions of the compound Burgers–Korteweg–de Vries equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 352(2), pages 419-435.
    3. David, Claire & Sagaut, Pierre, 2009. "Spurious solitons and structural stability of finite-difference schemes for non-linear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 655-660.
    4. David, Claire & Sagaut, Pierre, 2009. "Structural stability of finite dispersion-relation preserving schemes," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2193-2199.
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    Cited by:

    1. Nemati, Maedeh & Shateri Najaf Abady, Ali Reza & Toghraie, Davood & Karimipour, Arash, 2018. "Numerical investigation of the pseudopotential lattice Boltzmann modeling of liquid–vapor for multi-phase flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 489(C), pages 65-77.

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