Lattice Boltzmann simulation of some nonlinear complex equations

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4487 LNCS, Issue , 2007, Pages 818-825

  Shi, Baochang ^a  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Klein Gordon equation; Klein Gordon Schr dinger equations; Lattice Boltzmann method; Nonlinear Schr dinger equation

Indexed keywords

COMPUTER SIMULATION; PROBLEM SOLVING; SCHRODINGER EQUATION;

KLEIN-GORDON EQUATION; KLEIN-GORDON-SCHRÖDINGER EQUATIONS; LATTICE BOLTZMANN METHOD;

NONLINEAR EQUATIONS;

EID: 37248998527     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-72584-8_108     Document Type: Conference Paper

References (21)

1. Qian, Y. H., Succi, S., Orszag, S.: Recent advances in lattice Boltzmann computing. Annu. Rev. Comput. Phys. 3 (1995) 195-242
2. Dawson, S. P., Chen S. Y., Doolen,G. D.: Lattice Boltzmann computations for reaction-diffusion equations. J. Chem. Phys. 98 (1993) 1514-1523
3. Chopard, B., Droz, M.: Cellular automata modeling of physical systems. Cambridge University Press, Cambridge (1998)
4. Blaak, R., Sloot, P. M.: Lattice dependence of reaction-diffusion in lattice Boltzmann modeling. Comput. Phys. Comm. 129 (2000) 256-266
5. Van der Sman, R. G. M., Ernst, M. H.: Advection-diffusion lattice Boltzmann scheme for irregular lattices. J. Comput. Phys. 160(2) (2000) 766-782
6. Deng, B., Shi, B. C., Wang, G. C.: A new lattice Bhatnagar-Gross-Krook model for convection-diffusion equation with a source term. Chin. Phys. Lett. 22 (2005) 267-270
7. Yu, X. M., Shi, B. C.: A lattice Bhatnagar-Gross-Krook model for a class of the generalized Burgers equations. Chin. Phys. 25(7) (2006) 1441-1449
8. Yan, G. W.: A lattice Boltzmann equation for waves. J. Comput. Phys. (2000) 161(9) (2000) 61-69
9. Ginzburg, I.: Equilibrium-type and link-type lattice Boltzmann models for generic advection and anisotropic-dispersion equation. Advances in Water Resources. 28(11) (2005) 1171-1195
10. Meyer, D. A.: From quantum cellular automata to quantum lattice gas. J. Stat. Phys. 85 (1996) 551-574
11. Succi, S., Benzi, R.: The lattice Boltzmann equation for quantum mechanics. Physica D 69 (1993) 327-332
12. Succi, S.: Numerical solution of the Schrödinger equation using discrete kinetic theory. Phys. Rev. E 53 (1996) 1969-1975
13. Boghosian, B. M., Taylor IV, W.: Quantum lattice gas models for the many-body Schrödinger equation. Int. J. Mod. Phys. C 8 (1997) 705-716
14. Yepez, J., Boghosian, B.: An efficient and accurate quantum lattice-gas model for the many-body Schrödinger wave equation. Comput. Phys. Commun. 146 (2002) 280-294
15. Yepez, J.: Quantum lattice-gas model for the Burgers equation. J. Stat. Phys. 107 (2002) 203-224
16. Vahala, G., Yepez, J., Vahala, L.: Quantum lattice gas representation of some classical solitons. Phys. Lett. A 310 (2003) 187-196
17. Vahala, G., Vahala, L., Yepez, J: Quantum lattice representations for vector solitons in external potentials. Physica A 362 (2006) 215-221
18. Zhong, L. H., Feng, S. D., Dong, P., et al.: Lattice Boltzmann schemes for the nonlinear Schrödinger equation. Phys. Rev. E. 74 (2006) 036704-1-9
19. Xu, Y., Shu, C.-W.: Local discontinuous Galerkin methods for nonlinear Schrödinger equations. J. Comput. Phys. 205 (2005) 72-97
20. Kong, L. H., Liu, R. X., Xu, Z. L.: Numerical solution of interaction between Schrödinger field and Klein-Gordon field by multisymplectic method. Appl. Math. Comput. 181 (2006) 242-350
21. Guo, Z. L., Zheng, C. G., Shi, B. C.: Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method. Chin. Phys. 11 (2002) 366-374