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Entropy 2019, 21(4), 390; https://doi.org/10.3390/e21040390

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

1
College of Mathematics and Informatics, FJKLMAA, Fujian Normal University, Fuzhou 350117, China
2
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
*
Author to whom correspondence should be addressed.
Received: 13 March 2019 / Revised: 3 April 2019 / Accepted: 9 April 2019 / Published: 11 April 2019
(This article belongs to the Special Issue Thermodynamics of Non-Equilibrium Gas Flows)
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Abstract

In this work, we develop a mesoscopic lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model to solve (2 + 1)-dimensional wave equation with the nonlinear damping and source terms. Through the Chapman-Enskog multiscale expansion, the macroscopic governing evolution equation can be obtained accurately by choosing appropriate local equilibrium distribution functions. We validate the present mesoscopic model by some related issues where the exact solution is known. It turned out that the numerical solution is in very good agreement with exact one, which shows that the present mesoscopic model is pretty valid, and can be used to solve more similar nonlinear wave equations with nonlinear damping and source terms, and predict and enrich the internal mechanism of nonlinearity and complexity in nonlinear dynamic phenomenon. View Full-Text
Keywords: lattice Boltzmann BGK model; Chapman-Enskog expansion; nonlinear damping; wave equation; hyperbolic telegraph equation; sine-Gordon equation lattice Boltzmann BGK model; Chapman-Enskog expansion; nonlinear damping; wave equation; hyperbolic telegraph equation; sine-Gordon equation
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Li, D.; Lai, H.; Shi, B. Mesoscopic Simulation of the (2 + 1)-Dimensional Wave Equation with Nonlinear Damping and Source Terms Using the Lattice Boltzmann BGK Model. Entropy 2019, 21, 390.

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