A lattice Boltzmann model with an amending function forsimulating nonlinear partial differential equations

doi:10.1088/1674-1056/19/1/010504

中国物理B ›› 2010, Vol. 19 ›› Issue (1): 10504-010504.doi: 10.1088/1674-1056/19/1/010504

A lattice Boltzmann model with an amending function forsimulating nonlinear partial differential equations

陈林婕, 马昌凤

School of Mathematics and Computer Sciences, Fujian Normal University, Fuzhou 350007, China

收稿日期:2009-05-09 修回日期:2009-05-20 出版日期:2010-01-15 发布日期:2010-01-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10661005) and Fujian Province Science and Technology Plan Item (Grant No. 2008F5019).

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

Received:2009-05-09 Revised:2009-05-20 Online:2010-01-15 Published:2010-01-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10661005) and Fujian Province Science and Technology Plan Item (Grant No. 2008F5019).

摘要/Abstract

摘要： This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form $u_t+\alpha uu_{xx}+\beta u^n u_x+\gamma u_{xxx}+\xi u_{xxxx}=0$. 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.

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.

Key words: nonlinear partial differential equation, lattice Boltzmann method, Chapman--Enskog expansion, Taylor expansion

中图分类号: (Transport processes)

05.60.-k

02.60.Lj (Ordinary and partial differential equations; boundary value problems) 05.45.Yv (Solitons)

陈林婕, 马昌凤. A lattice Boltzmann model with an amending function forsimulating nonlinear partial differential equations[J]. 中国物理B, 2010, 19(1): 10504-010504.

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[J]. Chin. Phys. B, 2010, 19(1): 10504-010504.

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A lattice Boltzmann model with an amending function forsimulating nonlinear partial differential equations

A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

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