A lattice Boltzmann model for the nonlinear thermistor equations

Jiao Liu, Zhenhua Chai and Baochang Shi
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Jiao Liu: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China
Zhenhua Chai: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China
Baochang Shi: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 03, 1-16

Abstract: In this paper, we propose a general and efficient lattice Boltzmann (LB) model for solving the nonlinear thermistor equations, where the nonlinear diffusion and Poisson equations are solved by two LB equations. Through Chapman–Enskog analysis, the nonlinear thermistor equations can be recovered correctly from the present LB model. We then test the model through some numerical simulations, and find that the numerical results are in good agreement with analytical solutions. Additionally, the numerical results also show that the present LB model has a second-order convergence rate in space.

Keywords: Nonlinear thermistor equations; lattice Boltzmann model; Chapman–Enskog analysis (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0129183120500436

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