Li Demei, Lai Huilin, Lin Chuandong
College of Mathematics and Informatics, FJKLMAA, Fujian Normal University, Fuzhou 350007, China.
Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, China.
Entropy (Basel). 2019 May 28;21(6):542. doi: 10.3390/e21060542.
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.
本文通过耦合介观玻尔兹曼方程，提出了一种用于耦合正弦 - 戈登方程二元系统的新型格子玻尔兹曼模型。通过查普曼 - 恩斯科格多尺度展开，选择合适的离散平衡分布函数和修正函数，可以正确恢复宏观控制演化系统。该介观模型已通过几个具有解析解的相关问题得到验证。实验结果表明，数值结果与解析解一致。从介观角度来看，本方法为研究工程和科学自然非线性现象中出现的复杂非线性偏微分方程提供了一种新途径。
