Numerical schemes obtained from lattice Boltzmann equations for advection diffusion equations

International Journal of Modern Physics C

Volumn 17, Issue 11, 2006, Pages 1563-1577

  Suga, Shinsuke ^a  

^a NATIONAL INSTITUTE FOR ENVIRONMENTAL STUDIES   (Japan)

Author keywords

Accuracy of the scheme; Advection diffusion; Lattice Boltzmann equation; Stability of the numerical scheme

Indexed keywords

EID: 33845944222     PISSN: 01291831     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129183106010030     Document Type: Article

References (17)

1. M. Sukop and D. Thorne. Lattice Boltzmann Modeling (Springer-Verlarg, Berlin, Heiderberg, 2006).
2. R. Blaak and P. Sloot, Comput. Phys. Commun. 129, 256 (2000).
3. H. Xiaoye, L. Ning and G. Byron, Molecular Simulation 25, 145 (2000).
4. X. Zhang, A. Bengough, J. Crawford and I. Young, Adv. Water Resour. 25, 1 (2002).
5. E. Flekkøy, Phys. Rev. E 47, 4247 (1993).
6. R. van der Sman and M. Ernst, J. Comput. Phys. 160, 766 (2000).
7. S. Dawson, S. Chen and G. Doolen, J. Chem. Phys. 98, 1514 (1993).
8. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Oxford University Press, New York, 2001).
9. D. Wolf-Gladrow, J. Stat. Phys. 79, 1023 (1995).
10. M. G. Ancona, J. Comput. Phys. 115, 107 (1994).
11. E. C. Dufort and S. P. Frankel, Math. Tables Other Aids Comput. 7, 135 (1953).
12. S. Chen, Z. Wang, X. Shan and G. Doolen, J. Stat. Phys. 68, 379 (1992).
13. Y. H. Qian, D. d'Humières and P. Lallemand, Europhys. Lett. 17, 479 (1992).
14. J. W. Thomas, Numerical Partial Difference Equations: Finite Difference Methods (Springer-Verlag, New York, 1995).
15. R. D. Richtmyer and K. W. Morton, Difference Methods for Initial-Value Problems (Interscience Publishers, New York, 1967).
16. T. Inamuro, M. Yoshino, H. Inoue, R. Mizuno and F. Ogino, J. Comput. Phys. 179, 201 (2002).
17. R. A. Horn and C. R. Johnson, Matrix Analysis (Cambrige University Press, New York, 1985).