Multiple-relaxation-time finite-difference lattice Boltzmann model for the nonlinear convection-diffusion equation

Chen, Xinmeng; Chai, Zhenhua; Shang, Jinlong; Shi, Baochang

doi:10.1103/physreve.104.035308

Cited by 5 publications

(5 citation statements)

References 55 publications

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“…In the directional Laplacian Perona-Malik model [42,43], smoothing is performed along the edge direction. Due to the flexibility of the LB method for anisotropic diffusion-advection [44][45][46][47], applications of LB schemes for the modifications of the Perona-Malik equation (especially for anisotropic extensions like the directional Laplacian method [42,43]) are of interest for future study.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

confidence: 99%

Hybrid Lattice Boltzmann Model for Nonlinear Diffusion and Image Denoising

Ilyin

2023

Mathematics

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“…These vectors were summed and averaged to derive the final weight vector, which was used to establish the relationship between the weights and predict event trends. The formula for calculating the weight vector w is given as w = (A•n)/∑(A•n) , where A is the assessment matrix and n is the normalisation result of the column vectors [ [37] , [38] , [39] , [40] , [41] , [42] , [43] , [44] , [45] ].…”

Section: Methodsmentioning

confidence: 99%

Continuous quality improvement project to reduce the downtime of medical linear accelerators: A case study at Zhejiang Cancer Hospital

Lu,

Wu,

Mao

et al. 2024

Heliyon

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“…It is noticed that (2.16) has the form of a convection-diffusion equation (CDE). In the adoption of LBM for solving the CDE (Shi & Guo 2009;Zhao et al 2020;Chen et al 2021;Wang et al 2021a;Chai, Shi & Zhan 2022), the nonlinear charge mobility term can be treated as a cross-diffusion term (Wang et al 2021a) or a convective term (Chai et al 2022); these two models show almost no difference in this problem. Here, we can build the LLBM for q by treating the nonlinear charge mobility term inspired by the work of Wang et al (2021a).…”

Section: Linearized Lattice Boltzmann Methodsmentioning

confidence: 99%

“…2020; Chen et al. 2021; Wang et al. 2021 a ; Chai, Shi & Zhan 2022), the nonlinear charge mobility term can be treated as a cross-diffusion term (Wang et al.…”

Section: Problem Statement and Governing Equationsmentioning

confidence: 99%

Stability and bifurcation of annular electro-thermo-convection

Luo

Jiang

et al. 2023

J. Fluid Mech.

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We numerically investigated the global linear instability and bifurcations in electro-thermo-convection (ETC) of a dielectric liquid confined in a two-dimensional (2-D) concentric annulus subjected to a strong unipolar injection. Seven kinds of solutions exist in this ETC system due to the complex bifurcations, i.e. saddle-node, subcritical and supercritical Hopf bifurcations. These bifurcation routes constitute at most four solution branches. Global linear instability analysis and energy analysis were conducted to explain the instability mechanism and transition of different solutions and to predict the local instability regions. The linearized lattice Boltzmann method (LLBM) for global linear instability analysis, first proposed by Pérez et al. (Theor. Comput. Fluid Dyn., vol. 31, 2017, pp. 643–664) to analyse incompressible flows, was extended here to solve the whole set of coupled linear equations, including the linear Navier–Stokes equations, the linear energy equation, Poisson's equation and the linear charge conservation equation. A multiscale analysis was also performed to recover the macroscopic linearized Navier–Stokes equations from the four different discrete lattice Boltzmann equations (LBEs). The LLBM was validated by calculating the linear critical value of 2-D natural convection; it has an error of 1.39% compared with the spectral method. Instability with global travelling wave behaviour is a unique behaviour in the annulus configuration electrothermohydrodynamic system, which may be caused by the baroclinity. Finally, the chaotic behaviour was quantitatively analysed through calculation of the fractal dimension and Lyapunov exponent.

show abstract

Multiple-relaxation-time finite-difference lattice Boltzmann model for the nonlinear convection-diffusion equation

Cited by 5 publications

References 55 publications

Hybrid Lattice Boltzmann Model for Nonlinear Diffusion and Image Denoising

Hybrid Lattice Boltzmann Model for Nonlinear Diffusion and Image Denoising

Continuous quality improvement project to reduce the downtime of medical linear accelerators: A case study at Zhejiang Cancer Hospital

Stability and bifurcation of annular electro-thermo-convection

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