Diffusion lattice Boltzmann scheme on a orthorhombic lattice

Journal of Statistical Physics

Volumn 94, Issue 1-2, 1999, Pages 203-217

  Van Der Sman, R G M ^a   Ernst, M H ^b  

^a WAGENINGEN UNIVERSITY   (Netherlands)

^b UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Diffusion; Eigenmode analysis; Lattice Boltzmann

Indexed keywords

EID: 0032623129     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1004515413793     Document Type: Article

References (17)

1. 1. R. Benzi, S. Succi, and M. Vergassola, The lattice Boltzmann equation: Theory and applications. Phys. Rep. 222(3):145-197, 1992.
2. 2. J. M. V. A. Koelman, A simple Lattice Boltzmann scheme for Navier Stokes fluid flow. Europhys. Lett. 15(6):603-607 (1991).
3. 3. E. G. Flekkoy, Lattice BGK model tor miscible fluids, Phys. Rev. E 47:4247 (1993).
4. 4. M. R. Swift et al., Lattice Boltzmann simulations of liquid fas and binairy fluid systems. Phys. Rev. E 54 (5):5041-5052 (1996).
5. 5. J. G. M. Eggels and J. A. Somers, Numerical simulation of free convective flow using the Lattice Boltzmann scheme, Int. J. Heat and Fluid Flow 15:357-364 (1996).
6. 6. S. Ponce-Dawson, S. Chen, and G. D. Doolen, Lattice Boltzmann computations for reaction-diffusion equations, J. Chem. Phys. 98 (2):1514-1523, 1993.
7. 7. D. Wolf-Gladrow, A Lattice Boltzmann equation for diffusion, J. Stat. Phys. 79(5/6): 1023-1032 (1995).
8. 8. C. Hirsch, Numerical Computation of Internal and External Flows (John Wiley & Sons, New York, 1990).
9. 9. S. P. Das, H. J. Bussemaker, and M. H. Ernst, Generalized hydrodynamics and dispersion relations in lattice gasses, Phys. Rev. E 48(1) (1993).
10. 10. O. Behrend, R. Harris, and P. B. Warren, Hydrodynamic behaviour of Lattice Boltzmann and Lattice Bhatnagar Gross-Krook models, Phys. Rev E. 50(6), 4586-4595 (1994).
11. 11. U. Frisch, D. d'Humieres D., B. Hasslacher, Y. Pomeau, and J. P. Rivet, Lattice gas hydrodynamics in two and three dimensions, Complex Systems 1:649-707 (1987). See also, Lattice Gas Methods for Partial Differential Equations, G. D. Doolen, ed. (Addison-Wesley, 1989), p. 75.
12. 11. U. Frisch, D. d'Humieres D., B. Hasslacher, Y. Pomeau, and J. P. Rivet, Lattice gas hydrodynamics in two and three dimensions, Complex Systems 1:649-707 (1987). See also, Lattice Gas Methods for Partial Differential Equations, G. D. Doolen, ed. (Addison-Wesley, 1989), p. 75.
13. 12. G. McNamara and B. Alder, Analysis of the Lattice Boltzmann treatment of hydrodynamics, Physica A 194:218-228 (1993).
14. 13. R. Brito, M. H. Ernst, and T. R. Kirkpatrick, Staggered diffusivities in lattice gas cellular automata, J. Stat. Phys. 62:283 (1992).
15. 14. Y. H. Qian, D. d'Humieres, and P. Lallemand, Lattice BGK models for Navier-Stokes equation, Europhys. Lett. 17 (6):479-484 (1992).
16. 15. X. He, L. S. Luo, and M. Dembo, Some progress in Lattice Boltzmann method. Part I. Non-uniform mesh grids, J. Comp. Phys. 129:357-363 (1996).
17. 16. N. Cao, S. Chen, S. Jin, and D. Martinez, Physical symmetry and lattice symmetry in the Lattice Boltzmann method, Phys. Rev. E 55 (1):R21-R24 (1997).