Lattice Boltzmann model for generalized nonlinear wave equations
Lattice Boltzmann model for generalized nonlinear wave equations
复制标题
广义非线性波动方程的格子玻尔兹曼模型
DOI：
10.1103/physreve.84.046708
复制
发表时间：
2011-10-24
影响因子：
2.4
通讯作者：
Ma, Changfeng
中科院分区：
文献类型：
--
作者：
Lai, Huilin;Ma, Changfeng
本文利用格子Boltzmann模型求解一类非线性波动方程。通过选取适当的平衡分布函数和修正函数，利用Chapman-Enskog展开式，可以正确地恢复控制演化方程.我们验证了一些问题的解析解，包括二阶电报方程，非线性Klein-Gordon方程，阻尼，驱动sine-Gordon方程的算法。数值结果与解析解吻合较好，表明该算法是非常有效的，可用于求解更一般的非线性问题。
In this paper, a lattice Boltzmann model is developed to solve a class of the nonlinear wave equations. Through selecting equilibrium distribution function and an amending function properly, the governing evolution equation can be recovered correctly according to our proposed scheme, in which the Chapman-Enskog expansion is employed. We validate the algorithm on some problems where analytic solutions are available, including the second-order telegraph equation, the nonlinear Klein-Gordon equation, and the damped, driven sine-Gordon equation. It is found that the numerical results agree well with the analytic solutions, which indicates that the present algorithm is very effective and can be used to solve more general nonlinear problems.