- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Lattice Boltzmann model for wave propagation

Jianying Zhang, Guangwu Yan*, and Xiubo Shi

  • College of Mathematics, Jilin University, Changchun 130012, People’s Republic of China

  • *Corresponding author; yangw@email.jlu.edu.cn
PDF

Phys. Rev. E 80, 026706 – Published 27 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.026706

Abstract

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.

View figure in article

Article Text

References (59)

  1. U. Frisch, B. Hasslacher, and Y. Pomeau, Phys. Rev. Lett. 56, 1505 (1986).
  2. U. Frisch et al., Complex Syst. 1, 649 (1987).
  3. F. J. Higuera, S. Succi, and R. Benzi, Europhys. Lett. 9, 345 (1989).
  4. Y. H. Qian, D. d'Humieres, and P. Lallemand, Europhys. Lett. 17, 479 (1992).
  5. H. D. Chen, S. Y. Chen, and M. H. Matthaeus, Phys. Rev. A 45, R5339 (1992).
  6. R. Benzi, S. Succi, and M. Vergassola, Phys. Rep. 222, 145 (1992).
  7. S. Y. Chen and G. D. Doolen, Annu. Rev. Fluid Mech. 30, 329 (1998).
  8. X. W. Shan and H. D. Chen, Phys. Rev. E 49, 2941 (1994).
  9. M. Swift, W. Osborn, and J. Yeomans, Phys. Rev. Lett. 75, 830 (1995).
  10. K. N. Premnath and J. Abraham, J. Comput. Phys. 224, 539 (2007).
  11. A. K. Gunstensen, D. H. Rothman, S. Zaleski, and G. Zanetti, Phys. Rev. A 43, 4320 (1991).
  12. D. J. Holdych, J. G. Georgiadis, and R. O. Buckius, Phys. Fluids 13, 817 (2001).
  13. M. R. Swift et al., Phys. Rev. E 54, 5041 (1996).
  14. S. Succi, E. Foti, and F. J. Higuera, Europhys. Lett. 10, 433 (1989).
  15. A. Ladd, J. Fluid Mech. 271, 311 (1994).
  16. O. Filippova and D. Hanel, Comput. Fluids 26, 697 (1997).
  17. X. F. Pan, A. G. Xu, G. C. Zhang, and S. Jiang, Int. J. Mod. Phys. C 18, 1747 (2007).
  18. F. L. Hinton, M. N. Rosebblush, S. K. Wang, Y. R. Lin-Liu, and R. L. Miller, Phys. Rev. E 63, 061212 (2001).
  19. T. Kataoka and M. Tsutahara, Phys. Rev. E 69, 056702 (2004).
  20. M. Bernaschi, S. Succi, and H. Chen, J. Sci. Comput. 16, 135 (2001).
  21. Z. L. Guo, T. S. Zhao, and Y. Shi, Phys. Rev. E 70, 066706 (2004).
  22. A. C. Velivelli and K. M. Bryden, Physica A 362, 139 (2006).
  23. Y. L. Duan and R. X. Liu, Comput. Appl. Math. 206, 432 (2007).
  24. G. W. Yan and J. Y. Zhang, Math. Comput. Simul. 79, 1554 (2009).
  25. G. W. Yan and L. Yuan, Physica D 154, 43 (2001).
  26. S. Succi, Physica D 69, 327 (1993).
  27. S. Succi, Comput. Phys. Commun. 146, 317 (2002).
  28. S. Palpacelli and S. Succi, Phys. Rev. E 75, 066704 (2007).
  29. L. H. Zhong, S. D. Feng, P. Dong, and S. T. Gao, Phys. Rev. E 74, 036704 (2006).
  30. Z. H. Chai and B. C. Shi, Appl. Math. Model. 32, 2050 (2008).
  31. M. R. Wang, J. K. Wang, and S. Y. Chen, J. Comput. Phys. 226, 836 (2007).
  32. H. D. Chen, S. Y. Chen, G. Doolen, and Y. C. Lee, Complex Syst. 2, 259 (1988).
  33. C. Vanneste, P. Sebbah, and D. Sommette, Europhys. Lett. 17, 715 (1992).
  34. J. Buick, W. Easson, and C. Greated, Int. J. Numer. Methods Fluids 26, 657 (1998).
  35. P. J. McKerrow, S. M. Zhu, and S. New, IEEE Trans. Rob. Autom. 17, 202 (2001).
  36. B. James et al., International Conference on Supercomputing Proceedings of the Seventh International Conference on Supercomputing, Tokyo, Japan, 1993 (unpublished), pp. 348–356.
  37. D. Rothmann, Geophys. Res. Lett. 14, 17 (1987).
  38. J. I. Huang, Y. H. Chu, and C. S. Yin, Geophys. Res. Lett. 15, 1239 (1988).
  39. L. J. Huang and P. Mora, Geophys. J. Int. 119, 766 (1994).
  40. B. Chopard and P. O. Luthi, Theor. Comput. Sci. 217, 115 (1999).
  41. G. W. Yan, J. Comput. Phys. 161, 61 (2000).
  42. Y. W. Kwon and S. Hosoglu, Comput. Struct. 86, 663 (2008).
  43. W. S. Jiaung and J. R. Ho, Phys. Rev. E 77, 066710 (2008).
  44. J. M. Buick and J. A. Cosgrove, J. Phys. A 39, 13807 (2006).
  45. P. J. Dellar, Phys. Rev. E 65, 036309 (2002).
  46. H. Y. Li and H. Ki, Phys. Rev. E 76, 066707 (2007).
  47. J. M. Buick, J. A. Cosgrove, and C. A. Greated, Appl. Math. Model. 28, 183 (2004).
  48. P. Mora, J. Stat. Phys. 68, 591 (1992).
  49. J. M. Buick, Phys. Rev. E 76, 036713 (2007).
  50. F. Qiu, F. Xu, Z. Fan, and N. Neophytos, IEEE Trans. Vis. Comput. Graph. 13, 1576 (2007).
  51. Y. Zhao et al., IEEE Trans. Vis. Comput. Graph. 13, 179 (2007).
  52. Tosiya Taniuti and Katsunobu Nishihara, Nonlinear Waves (Pitman, Boston, 1983).
  53. G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974).
  54. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gas (Cambridge University Press, Cambridge, 1970).
  55. D. Holdych et al., J. Comput. Phys. 193, 595 (2004).
  56. C. W. Hirt, J. Comput. Phys. 2, 339 (1968).
  57. J. Wang and R. X. Liu, J. Comput. Appl. Math. 134, 59 (2001).
  58. G. Fairweather and A. R. Mitchell, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 4, 163 (1967).
  59. D. Halliday and R. Resnick, Physics, 3rd edition (Wiley, New York, 1978), Pt. II.

Outline

Information

Phys. Rev. E 80, 026706– Published 27 August, 2009
  • Received 10 October 2008

© 2009 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation