Lattice Boltzmann model for two-dimensional generalized sine-Gordon equation |
| |
Authors: | Yali Duan Linghua Kong Xianjin Chen and Min Guo |
| |
Institution: | School of Mathematical sciences, University of Science and Technology of China, Hefei, Anhui 230026, China,School of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi, 330022, China,School of Mathematical sciences, University of Science and Technology of China, Hefei, Anhui 230026, China and Department of Basic, North China College of Mechanics and Electrics, Changzhi, Shanxi, 046000, China |
| |
Abstract: | The nonlinear sine-Gordon equation arises in various problems in science and engineering. In this paper, we propose a numerical model based on lattice Boltmann method to obtain the numerical solutions of two-dimensional generalized sine-Gordon equation, including damped and undamped sine-Gordon equation. By choosing properly the conservation condition between the macroscopic quantity $u_t$ and the distribution functions and applying
the Chapman-Enskog expansion, the governing equation is recovered correctly from the lattice Boltzmann equation. Moreover, the local equilibrium distribution function is obtained. The numerical results of the first three examples agree well with the analytic solutions, which indicates the lattice Boltzmann model is satisfactory and efficient. Numerical solutions for cases involving the most known from the bibliography line and ring solitons are given. Numerical experiments also show that the present scheme has a good long-time numerical behavior for the generalized sine-Gordon equation. Moreover, the model can also be applied to other two-dimensional nonlinear wave equations, such as nonlinear hyperbolic telegraph equation and Klein-Gordon equation. |
| |
Keywords: | Lattice Boltzmann method Sine-Gordon equation Chapman-Enskog expansion soliton |
|
| 点击此处可从《Journal of Applied Analysis & Computation》浏览原始摘要信息 |
| 点击此处可从《Journal of Applied Analysis & Computation》下载免费的PDF全文 |
|