Zhang Jianying, Yan Guangwu, Shi Xiubo
College of Mathematics, Jilin University, Changchun 130012, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 2):026706. doi: 10.1103/PhysRevE.80.026706. Epub 2009 Aug 27.
A lattice Boltzmann model for two-dimensional wave equation is proposed by using the higher-order moment method. The higher-order moment method is based on the solution of a series of partial differential equations obtained by using multiscale technique and Chapman-Enskog expansion. In order to obtain the lattice Boltzmann model for the wave equation with higher-order accuracy of truncation errors, we removed the second-order dissipation term and the third-order dispersion term by employing the moments up to fourth order. The reversibility in time appears owing to the absence of the second-order dissipation term and the third-order dispersion term. As numerical examples, some classical examples, such as interference, diffraction, and wave passing through a convex lens, are simulated. The numerical results show that this model can be used to simulate wave propagation.
利用高阶矩方法提出了一种二维波动方程的格子玻尔兹曼模型。高阶矩方法基于通过多尺度技术和查普曼 - 恩斯科格展开得到的一系列偏微分方程的解。为了获得截断误差具有高阶精度的波动方程的格子玻尔兹曼模型，我们通过采用四阶矩消除了二阶耗散项和三阶色散项。由于二阶耗散项和三阶色散项的缺失，时间上的可逆性出现了。作为数值例子，模拟了一些经典例子，如干涉、衍射以及波通过凸透镜的情况。数值结果表明该模型可用于模拟波的传播。
