Lattice Boltzmann method for the generalized Kuramoto-Sivashinsky equation

Physica A: Statistical Mechanics and its Applications

Volumn 388, Issue 8, 2009, Pages 1405-1412

  Lai, Huilin ^a   Ma, Changfeng ^a,b  

^a FUJIAN NORMAL UNIVERSITY   (China)

^b GUILIN UNIVERSITY OF ELECTRONIC TECHNOLOGY   (China)

Author keywords

Chapman Enskog expansion; Generalized Kuramoto Sivashinsky equation; KdV Burgers Kuramoto equation; Lattice Boltzmann method

Indexed keywords

KINETIC THEORY; PARTIAL DIFFERENTIAL EQUATIONS;

CHAPMAN-ENSKOG EXPANSION; EVOLUTION EQUATIONS; KDV-BURGER; KURAMOTO-SIVASHINSKY EQUATIONS; LATTICE BOLTZMANN METHOD; LATTICE BOLTZMANN MODELS; NUMERICAL RESULTS;

BOLTZMANN EQUATION;

EID: 59449088152     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2009.01.005     Document Type: Article

References (39)

1. Gary doolen. Lattice gas and lattice Boltzmann for partial differential equation. Physica D 47 (1991) 3-339
2. Lebowitz J.L., Orszag S.A., and Qian Y.H. Program of the lattice gas'94 meeting at Princeton. J. Statist. Phys. 81 (1995) 1-536
3. Benzi R., Succi S., and Vergasola M. The lattice Boltzmann equation: Theory and application. Phys. Rep. 222 (1992) 145
4. Chen S.Y., and Doolen G.D. Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30 (1998) 329
5. Guo Z.L., Zheng C.G., and Shi B.C. Thermal lattice Boltzmann equation for low Mach number flows: Decoupling model. Phys. Rev. E 75 (2007) 036704
6. Özer S., and Kutluay S. An analytical-numerical method for solving the Koreweg-de Vries equation. Appl. Math. Comput. 164 (2005) 789-797
7. Helal M.A., and Mehanna M.S. A comparison between two different methods for solving KdV-Burgers equation. Chaos Solitions Fractals 28 (2006) 320-326
8. Kutluay S., Bahadir A.R., and Özeş A. A small time solutions for the Korteweg-de Vries equation. Appl. Math. Comput. 107 (2000) 203-210
9. Geyikli T., and Kaya D. An application for a modified KdV equation by the decomposition method and finite element method. Appl. Math. Comput. 169 (2005) 971-981
10. Helal M.A. A Chebyshev spectral method for solving Korteweg-de Vries equation with hydrodynamical application. Chaos Solitions Fractals 12 (2001) 943-950
11. Soliman A.A. A numerical simulation and explicit solutions of KdV-Burgers and Lax's seventh-order KdV equations. Chaos Solitions Fractals 29 (2006) 294-302
12. Qian Y. Simulating thermohydrodynamics with lattice BGK models. J. Sci. Comput. 8 (1993) 231-241
13. Shi B.C., Guo Z.L., and Wang N.C. Lattice-Bhatnagar-Cross-Krook simulations of turbulent natural convection in a cavity. Chinese Phys. Lett. 19 (2002) 515-517
14. Sun C.H. Lattice-Boltzmann models for high speed flows. Phys. Rev. E 58 (1998) 7283
15. Guo Z.L., and Zhao T.S. Lattice Boltzmann model for incompressible flows through porous media. Phys. Rev. E 66 (2002) 036304
16. Xu Y.S., Zhong Y.j., and Huang G.X. Lattice Boltzmann method for diffusion-reaction-transport pocesses in heterogeneous porous media. Chinese Phys. Lett. 21 (2004) 1298-1301
17. Ladd A.J.D., and Verberg R. Lattice-Boltzmann simulations of particle-fluid suspensions. J. Statist. Phys. 104 (2001) 1191-1251
18. Fang H.P., and Chen S.Y. Lattice Boltzmann method for three-dimensional moving particles in a Newtonian fluid. Chinese Phys. 13 (2004) 47-53
19. Larkin N.A. Korteweg-de Vries and Kuramoto-Sivashinsky equations in bounded domains. J. Math. Anal. Appl. 297 (2004) 169-185
20. Khater A.H., and Temsah R.S. Numerical solutions of the generalized Kuramoto-Sivashinsky equation by Chebyshev spectral collocation methods. Comput. Math. Appl. 03 (2008) 013
21. Topper J., and Kawahara T. Approximate equations for long nonlinear waves on a viscous fluid. Physical Society of Japan, J. 44 (1978) 663-666
22. T. Tatsumi, Irregularity, regularity and singularity of turbulence. Turbulence and chaotic phenomena in fluids, Iutam (1984) 1-10
23. Saprykin S., Demekhin E.A., and Kalliadasis S. Two-dimensional wave dynamics in thin films.I.Stationary solitary pulses. Phys. Fluids 17 (2005) 117105
24. Hooper A.P., and Grimshaw R. Nonlinear instability at the interface between two viscous fluids. Phys. Fluids 28 (1985) 37-45
25. Kuramoto Y., and Tsuzuki T. Persistent propagation of concentration waves in dissipative media far from thermal equilibrium. Progr. Theoret. Phys. 55 (1976) 356
26. Sivashinsky G.I. Instabilities, pattern-formation, and turbulence in flames. Annv. Rev. Fluid Mech. 15 (1983) 179-199
27. Grimshaw R., and Hooper A.P. The non-existence of a certain class of travelling wave solutions of the Kuramoto-Sivashinsky equation. Physica D 50 (1991) 231-238
28. Liu X. Gevrey class regularity and approximate inertial manifolds for the Kuramoto-Sivashinsky equation. Physica D 50 (1991) 135-151
29. Xua Y., and Shu C.-W. Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations. Comput. Methods Appl. Mech. Engrg 195 (2006) 3430-3447
30. Fan E. Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277 (2000) 212-218
31. yang T.-S. On traveling-wave solutions of the Kuramoto-Sivashinsky equation. Physica D 110 (1997) 25-42
32. Chen H., and Zhang H. New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation. Chaos Solitions Fractals 19 (2004) 71-76
33. Bernsdorf J., Jaekela U., Zeiserb T., Doic S., Takeic T., Matsumotod H., and Nishizawad K. Numerical simulation of reaction-diffusion and adsorption processes in porous media using lattice boltzmann methods with concurrent visualisation. Parallel Comput. Fluid Dyn. 2003 (2002) 233-240
34. Duan Y., Liua R., and Jiang Y. Lattice Boltzmann model for the modified Burgers'equation. Appl. Math. Comput. 202 2 (2008) 489-497
35. Ma C.F. A new lattice Boltzmann model for KdV-Burgers equation. Chinese Phys. Lett. 22 9 (2005) 2313-2315
36. Zhong L., Feng S., and Dong P. Lattice Boltzmann schemes for the nonlinear Schrodinger equation. Phys. Rev. E 74 (2006) 036704
37. Ma C.F., and Shi B.C. Lattice Bhatnagar-Gross-Krook simulations of hydromagnetic double-diffusive convection in a rectangular enclosure with opposing temperature and concentration gradients. Chinese Phys. Lett. 23 7 (2006) 1842-1845
38. Ma C.F., Tang J., and Chen X.H. Lattice BGK Model for Simulating MKDV Equation. Chinese J. Appl. Mech. 24 4 (2007) 519-521 (in Chinese)
39. Guo Z.L., Zheng C.G., and Shi B.C. Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method. Chinese Phys. 11 4 (2002) 366-374