The lattice Boltzmann model for the second-order Benjamin–Ono equations
作者： Huilin Lai , Changfeng Ma
DOI: 10.1088/1742-5468/2010/04/P04011
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摘要: In this paper, in order to extend the lattice Boltzmann method deal with more complicated nonlinear equations, we propose a 1D scheme an amending function for second-order (1 + 1)-dimensional Benjamin–Ono equation. With Taylor expansion and Chapman–Enskog expansion, governing evolution equation is recovered correctly from continuous The equilibrium distribution are obtained. Numerical simulations carried out 'good' Boussinesq 'bad' one validate proposed model. It found that numerical results agree well analytical solutions. present model can be used solve kinds of partial differential equations.
sci-hub.se 参考文章(38)
Vivette Girault, Pierre-Arnaud Raviart, Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms ,(1986)
Zhen-hui Xu, Da-quan Xian, Han-lin Chen, New periodic solitary-wave solutions for the Benjiamin Ono equation Applied Mathematics and Computation. ,vol. 215, pp. 4439- 4442 ,(2010) , 10.1016/J.AMC.2009.11.009
Ma Chang-Feng, Shi Bao-Chang, Lattice Bhatnagar Gross Krook Simulations of Hydromagnetic Double-Diffusive Convection in a Rectangular Enclosure with Opposing Temperature and Concentration Gradients Chinese Physics Letters. ,vol. 23, pp. 1842- 1845 ,(2006) , 10.1088/0256-307X/23/7/052
Stanley J. Farlow, Stephen F. Becker, Partial differential equations for scientists and engineers American Journal of Physics. ,vol. 53, pp. 702- 702 ,(1985) , 10.1119/1.14292
Baochang Shi, Zhaoli Guo, Lattice Boltzmann model for nonlinear convection-diffusion equations. Physical Review E. ,vol. 79, pp. 016701- ,(2009) , 10.1103/PHYSREVE.79.016701
Vladimir V. Varlamov, Long-time asymptotics of solutions of the second initial-boundary value problem for the damped Boussinesq equation Abstract and Applied Analysis. ,vol. 2, pp. 281- 299 ,(1997) , 10.1155/S1085337597000407
R. Benzi, S. Succi, M. Vergassola, The lattice Boltzmann equation: theory and applications Physics Reports. ,vol. 222, pp. 145- 197 ,(1992) , 10.1016/0370-1573(92)90090-M
Peter A. Clarkson, Martin D. Kruskal, New similarity reductions of the Boussinesq equation Journal of Mathematical Physics. ,vol. 30, pp. 2201- 2213 ,(1989) , 10.1063/1.528613
Q Li, YL He, Y Wang, GH Tang, None, Three-dimensional non-free-parameter lattice-Boltzmann model and its application to inviscid compressible flows Physics Letters A. ,vol. 373, pp. 2101- 2108 ,(2009) , 10.1016/J.PHYSLETA.2009.04.036
D Levi, P Winternitz, Non-classical symmetry reduction: example of the Boussinesq equation Journal of Physics A. ,vol. 22, pp. 2915- 2924 ,(1989) , 10.1088/0305-4470/22/15/010