Volume 42 Issue 5
May  2021
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LI Mengjun, DAI Houping, WEI Xuedan, ZHENG Zhoushun. A Lattice Boltzmann Method for Spatial Fractional-Order Telegraph Equations[J]. Applied Mathematics and Mechanics, 2021, 42(5): 522-530. doi: 10.21656/1000-0887.410311
Citation: LI Mengjun, DAI Houping, WEI Xuedan, ZHENG Zhoushun. A Lattice Boltzmann Method for Spatial Fractional-Order Telegraph Equations[J]. Applied Mathematics and Mechanics, 2021, 42(5): 522-530. doi: 10.21656/1000-0887.410311

A Lattice Boltzmann Method for Spatial Fractional-Order Telegraph Equations

doi: 10.21656/1000-0887.410311
Funds:  The National Natural Science Foundation of China(51974377)
  • Received Date: 2020-10-15
  • Rev Recd Date: 2021-04-06
  • Publish Date: 2021-05-01
  • 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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