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Lattice Boltzmann methods for global linear instability analysis

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Abstract

Modal global linear instability analysis is performed using, for the first time ever, the lattice Boltzmann method (LBM) to analyze incompressible flows with two and three inhomogeneous spatial directions. Four linearization models have been implemented in order to recover the linearized Navier–Stokes equations in the incompressible limit. Two of those models employ the single relaxation time and have been proposed previously in the literature as linearization of the collision operator of the lattice Boltzmann equation. Two additional models are derived herein for the first time by linearizing the local equilibrium probability distribution function. Instability analysis results are obtained in three benchmark problems, two in closed geometries and one in open flow, namely the square and cubic lid-driven cavity flow and flow in the wake of the circular cylinder. Comparisons with results delivered by classic spectral element methods verify the accuracy of the proposed new methodologies and point potential limitations particular to the LBM approach. The known issue of appearance of numerical instabilities when the SRT model is used in direct numerical simulations employing the LBM is shown to be reflected in a spurious global eigenmode when the SRT model is used in the instability analysis. Although this mode is absent in the multiple relaxation times model, other spurious instabilities can also arise and are documented herein. Areas of potential improvements in order to make the proposed methodology competitive with established approaches for global instability analysis are discussed.

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Authors and Affiliations

  1. School of Aeronautics, Universidad Politécnica de Madrid, Madrid, Spain

    José Miguel Pérez

  2. School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, UK

    Alfonso Aguilar

  3. School of Engineering, The Quadrangle, The University of Liverpool, Brownlow Hill, Liverpool, L69 3GH, UK

    Vassilis Theofilis

  4. Theoretical and Applied Mechanics Laboratory, Department of Mechanical Engineering, Universidade Federal Fluminense, Rua Passo da Patria 156, Niterói, RJ, 24210-240, Brazil

    Vassilis Theofilis

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  1. José Miguel Pérez
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  2. Alfonso Aguilar
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  3. Vassilis Theofilis
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Correspondence to José Miguel Pérez.

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Communicated by Ati Sharma.

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Pérez, J.M., Aguilar, A. & Theofilis, V. Lattice Boltzmann methods for global linear instability analysis. Theor. Comput. Fluid Dyn. 31, 643–664 (2017). https://doi.org/10.1007/s00162-016-0416-7

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