Hydrodynamic limits and numerical errors of isothermal lattice Boltzmann schemes

Wissocq, Gauthier; Sagaut, Pierre

doi:10.1016/j.jcp.2021.110858

Cited by 18 publications

(8 citation statements)

References 87 publications

(285 reference statements)

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“…The enthalpy equation ( 4) is solved at the same time using a finite difference discretization under the non-conservative form, exactly as presented by Tayyab et al [36,37]. Second-order consistency to the macroscopic equations (1-4) can be shown via Chapman-Enskog [52], or Taylor [53,54] expansions.…”

Section: Lbm Description For Low-mach Number Approximationmentioning

confidence: 99%

Large eddy simulation of fire-induced flows using Lattice-Boltzmann methods

Taha,

Zhao,

Lamorlette

et al. 2024

International Journal of Thermal Sciences

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Section: Lbm Description For Low-mach Number Approximationmentioning

confidence: 99%

Large eddy simulation of fire-induced flows using Lattice-Boltzmann methods

Taha,

Zhao,

Lamorlette

et al. 2024

International Journal of Thermal Sciences

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“…Note that (11) is not exactly the Perona-Malik Equation (1) but one can demonstrate that its properties are very similar to (1). First, one needs to introduce an orthonormal frame consisting of two vectors: one vector defined by T is parallel to ∇I and another one N is perpendicular to ∇I.…”

Section: Lattice Boltzmann Scheme For Nonlinear Diffusionmentioning

confidence: 99%

“…Although one can take large time steps while modeling a diffusion process using conventional LB models, the limitations emerge from accuracy issues. For non-small values of the time step and diffusion coefficient, LB models suffer from hyper-viscous errors (or truncation errors) [7][8][9][10][11][12]. In order to improve the accuracy of LB schemes, several approaches can be adopted.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Lattice Boltzmann Model for Nonlinear Diffusion and Image Denoising

Ilyin

2023

Mathematics

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In the present paper, a novel approach for image denoising based on the numerical solution to the nonlinear diffusion equation is proposed. The Perona–Malik-type equation is solved by employing a hybrid lattice Boltzmann model with five discrete velocities. In this method, the regions with large values of the diffusion coefficient are modeled with the lattice Boltzmann scheme for which hyper-viscous defects are reduced, while other regions are modeled with the conventional lattice Boltzmann model. The new method allows us to solve Perona–Malik-type equations with relatively large time steps and good accuracy. In numerical experiments, the removal of salt and pepper, speckle and Gaussian noise is considered. For salt and pepper noise, the novel scheme yields better peak signal-to-noise ratios in image denoising problems compared to the standard lattice Boltzmann approach. For certain non-small values of time steps, the novel model shows better results for speckle and Gaussian noise on average.

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“…Given (i) the excellent dissipation properties of LBM for acoustic propagation [26], including for hybrid methods [12,13] for which vortical and acoustic mode propagations are convected by the LBM scheme [27][28][29] while species/entropy modes are convected with a specifically designed scheme [30,31] ; and (ii) the success encountered in simulating burners with complex geometries [23,25] for a reasonable cost, the next logical step is to investigate and develop LBM able to model thermo-acoustic instabilities.…”

Section: Introductionmentioning

confidence: 99%