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Improved multiple-relaxation-time lattice Boltzmann model for Allen–Cahn equation

Author

Listed:
  • Xianzhong Yan

    (School of Mathematics, Southeast University, Sipailou 2, Nanjing, Jiangsu, 210096, P. R. China)

  • Yonglong Ye

    (School of Information Science and Engineering, Southeast University, Sipailou 2, Nanjing, Jiangsu, 210096, P. R. China)

  • Jun Chen

    (School of Mathematics, Southeast University, Sipailou 2, Nanjing, Jiangsu, 210096, P. R. China)

  • Xiaofeng Wang

    (School of Mathematics, Southeast University, Sipailou 2, Nanjing, Jiangsu, 210096, P. R. China)

  • Rui Du

    (School of Mathematics, Southeast University, Sipailou 2, Nanjing, Jiangsu, 210096, P. R. China)

Abstract

Two-phase flow is important in both science and engineering. In this paper, a D2Q5 multi-relaxation-time lattice Boltzmann model is proposed for solving Allen–Cahn equation, which is a convection–diffusion equation for the order parameter. Through Chapmann–Enskog analysis, the macroscopic equations can be recovered from the D2Q5 MRT LB model. Then, a detailed numerical study on several classical problems is performed to give a comparison between the present model for the AC equation and the previous study. The results show that the present model gets better accuracy and has better stability than that of single-relaxation-time LB model, and has higher computational efficiency than that of D2Q9 MRT LB model. Furthermore, as an important application, the model is also used to study the deformation field problem because of its excellent ability to cope with complex and changeable boundaries.

Suggested Citation

  • Xianzhong Yan & Yonglong Ye & Jun Chen & Xiaofeng Wang & Rui Du, 2021. "Improved multiple-relaxation-time lattice Boltzmann model for Allen–Cahn equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 32(07), pages 1-14, July.
    • Handle: RePEc:wsi:ijmpcx:v:32:y:2021:i:07:n:s0129183121500868
    DOI: 10.1142/S0129183121500868
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