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Mesoscopic Simulation of the (2 + 1)-Dimensional Wave Equation with Nonlinear Damping and Source Terms Using the Lattice Boltzmann BGK Model

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# Mesoscopic Simulation of the Two-Component System of Coupled Sine-Gordon Equations with Lattice Boltzmann Method

1
College of Mathematics and Informatics, FJKLMAA, Fujian Normal University, Fuzhou 350007, China
2
Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, China
*
Authors to whom correspondence should be addressed.
Entropy 2019, 21(6), 542; https://doi.org/10.3390/e21060542
Received: 29 April 2019 / Revised: 22 May 2019 / Accepted: 25 May 2019 / Published: 28 May 2019
(This article belongs to the Special Issue Thermodynamics of Non-Equilibrium Gas Flows)
In this paper, a new lattice Boltzmann model for the two-component system of coupled sine-Gordon equations is presented by using the coupled mesoscopic Boltzmann equations. Via the Chapman-Enskog multiscale expansion, the macroscopical governing evolution system can be recovered correctly by selecting suitable discrete equilibrium distribution functions and the amending functions. The mesoscopic model has been validated by several related issues where analytic solutions are available. The experimental results show that the numerical results are consistent with the analytic solutions. From the mesoscopic point of view, the present approach provides a new way for studying the complex nonlinear partial differential equations arising in natural nonlinear phenomena of engineering and science. View Full-Text
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Li, D.; Lai, H.; Lin, C. Mesoscopic Simulation of the Two-Component System of Coupled Sine-Gordon Equations with Lattice Boltzmann Method. Entropy 2019, 21, 542.