Lattice Boltzmann methods for global linear instability analysis

Pérez, José Pedro López; Aguilar, Alfonso Zamorano; Theofilis, Vassilios

doi:10.1007/s00162-016-0416-7

Cited by 14 publications

(31 citation statements)

References 53 publications

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“…The coupled double-distribution-function LBM (Guo et al 2002a;Li et al 2007) is used for flow field and temperature field. Pérez et al (2017) first gave the linearization of the local equilibrium probability distribution function (PDF) for recovering the linear momentum equation without an external force. Then, we extend their methods to derive the linear energy equation (2.4c) from the lattice Boltzmann equation of the temperature field, and the coupled linearized lattice Boltzmann equation for the perturbation flow field and temperature field can be expressed as…”

Section: Linearized Navier-stokes Equation Derivationmentioning

confidence: 99%

“…Most previous instability analyses of the LBM have been focused on the numerical stability or robustness of the method itself. Only one work by Pérez, Aguilar & Theofilis (2017) regarded the LBM as a tool for linear instability analysis. In that work, the global stability of incompressible flows with two and three inhomogeneous spatial directions was considered using the LBM, and they found that the LBM could reproduce flow instability analysis results obtained by spectral methods (Theofilis 2000a).…”

Section: Introductionmentioning

confidence: 99%

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Global linear instability analysis of thermal convective flow using the linearized lattice Boltzmann method

et al. 2022

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Modal global linear stability analysis of thermal convection is performed with the linearized lattice Boltzmann method (LLBM). The onset of Rayleigh–Bénard convection in rectangular cavities with conducting and adiabatic sidewalls and the instability of two-dimensional (2-D) and three-dimensional (3-D) natural convection in cavities are studied. The method of linearizing the local equilibrium probability distribution function that was first proposed by Pérez et al. (Theor. Comp. Fluid Dyn., vol. 31, 2017, pp. 643–664) is extended to solve the coupled linear Navier–Stokes equations together with the linear energy equation in this work. A multiscale analysis is also performed to recover the macroscopic linear Navier–Stokes equations from the discrete lattice Boltzmann equations for both the single and multiple relaxation time models. The present LLBM is implemented in the framework of the Palabos library. It is validated by calculating the linear critical value of 2-D natural convection that the LLBM with the multiple relaxation time model has an error less than 1 % compared with the spectral method. The instability mechanism of the flow is explained by kinetic energy transfer analysis. It is shown that the buoyancy mechanism and inertial mechanism tend to stabilize the Hopf bifurcation of the 2-D natural convection at Pr < 0.08 and Pr > 1, respectively. For 3-D natural convection, subcritical bifurcation of the Hopf type is found for low-Prandtl-number fluids (Pr < 0.1).

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Section: Linearized Navier-stokes Equation Derivationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global linear instability analysis of thermal convective flow using the linearized lattice Boltzmann method

et al. 2022

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“…Linear stability analysis can also be directly performed in the lattice Boltzmann framework (see. [28,29]) however this approach is still in its infancy and is only applied to simple single fluid flow. In this study we carry out non linear simulation with the aforementioned lattice Boltzmann model and compute the growth rate of the perturbations.…”

Section: Early Times: Growth Rate Of the Perturbationmentioning

confidence: 99%

Simulation of Viscous Fingering Instability by the Lattice Boltzmann Method

Vienne

Marié

Grasso

2019

AIAA Aviation 2019 Forum

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The viscous fingering instability is successfully simulated within a lattice Boltzmann framework. Each species of the mixture is governed by its own kinetic equation and a force takes into account the diffusion between species. The influence of the porous medium is mimicked by using the gray lattice Boltzmann model or the Brinkman force model. In this study, both representations of the porous medium yield equivalent results. Then a physical analysis of the instability is performed and two different dynamical behaviour are stated and discussed. Finally, it is observed that a high Péclet number intensify the instability and the viscous dissipation stemming from the Darcy-Brinkman equations delay the development of the fingers in the case of large effective viscosity.

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“…Finally, contributions to numerical aspects of flow instability and control analysis presented in this volume include a criterion for optimal grid adaptation associated with error sensitivity to grid refinement [16], as well as a novel framework for the computation of unstable steady basic flows [8], alternative to the well-established selective frequency damping method [2]. A boundary condition for the collocated solution of the two-and three-dimensional eigenvalue problems on collocated grids was presented [32] and a framework for the stability analysis of flows obtained by Lattice Boltzman methods [24] was also discussed.…”

Section: Contributions To the Present Volumementioning

confidence: 99%

Special issue on global flow instability and control

Theofilis

Colonius

2017

Theor. Comput. Fluid Dyn.

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This special issue is the second on the topic of "Global Flow Instability and Control," following the first in 2011. As with the previous special issue, the participants of the last two symposia on Global Flow Instability and Control, held in Crete, Greece, were invited to submit publications. These papers were peer reviewed according to the standards of the journal, and this issue represents a snapshot of the progress since 2011. In this preface, a sampling of important developments in the field since the first issue is discussed. A synopsis of the papers in this issue is given in that context.

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Lattice Boltzmann methods for global linear instability analysis

Cited by 14 publications

References 53 publications

Global linear instability analysis of thermal convective flow using the linearized lattice Boltzmann method

Global linear instability analysis of thermal convective flow using the linearized lattice Boltzmann method

Simulation of Viscous Fingering Instability by the Lattice Boltzmann Method

Special issue on global flow instability and control

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