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A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations |
| Chen Lin-Jie(陈林婕) and Ma Chang-Feng(马昌凤)† |
| School of Mathematics and Computer Sciences, Fujian Normal University, Fuzhou 350007, China |
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Abstract This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form $u_t+\alpha uu_x+\beta u^n u_x+\gamma u_{xx}+\delta u_{xxx}+\zeta u_{xxxx}=0$. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman--Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions.
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Received: 09 May 2009
Revised: 20 May 2009
Accepted manuscript online:
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PACS:
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05.60.-k
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(Transport processes)
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02.60.Lj
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(Ordinary and partial differential equations; boundary value problems)
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05.45.Yv
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(Solitons)
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| Fund: Project supported by the National
Natural Science Foundation of China (Grant No. 10661005) and Fujian
Province Science and Technology Plan Item (Grant No. 2008F5019). |
Cite this article:
Chen Lin-Jie(陈林婕) and Ma Chang-Feng(马昌凤) A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations 2010 Chin. Phys. B 19 010504
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