A Lattice Boltzmann Method for Spatial Fractional-Order Telegraph Equations
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摘要: 应用格子Boltzmann方法(LBM)对RiemannLiouville空间分数阶电报方程进行了数值模拟研究.首先,将分数阶算子中的积分项进行离散化处理,并进行了收敛阶分析.然后,构建了带修正函数项的一维三速度(D1Q3)的LBM演化模型.利用ChapmanEnskog多尺度技术和Taylor展开技术,推导出各平衡态分布函数和修正函数的具体表达式,准确地从所建的演化模型恢复出宏观方程.最后,数值计算结果表明该模型是稳定、有效的.Abstract: The lattice Boltzmann method (LBM) was applied to numerically solve Riemann-Liouville spatial fractional-order telegraph equations. Firstly, the integral term of the fractional-order operator was discretized and the order of convergence was analyzed. Then, a 1D and 3-velocity (D1Q3) LBM evolution model with modified functions was established. The expressions of equilibrium distribution functions and correction functions were deduced by means of the Chapman-Enskog multi-scale analysis and the Taylor expansion technique. Therefore, the macroscopic equation was exactly recovered from the established evolution model. Numerical results show the stability and effectiveness of the model.
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