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

This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations （NPDEs） in the form ut ＋αuux ＋βu^nuz ＋γuxx ＋δuzxx ＋ζxxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of...

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Bibliographic Details
Published inChinese physics B Vol. 19; no. 1; pp. 148 - 155
Main Author 陈林婕 马昌凤
Format Journal Article
LanguageEnglish
Published IOP Publishing 2010
Subjects
Accuracy
Boltzmann equation
Boltzmann transport equation
Boltzmann方程
Computer simulation
Equivalence
Evolution
Lattices
Mathematical analysis
Mathematical models
Nonlinear differential equations
Nonlinearity
Partial differential equations
修正函数
功能模拟
格子Boltzmann模型
模型修改
演化方程
非线性偏微分方程
非线性项
Online AccessGet full text
ISSN1674-1056
2058-3834
DOI10.1088/1674-1056/19/1/010504

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Summary:This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations （NPDEs） in the form ut ＋αuux ＋βu^nuz ＋γuxx ＋δuzxx ＋ζxxxx = 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.
Bibliography:O35
O175.29
11-5639/O4
nonlinear partial differential equation, lattice Boltzmann method, Chapman-Enskog expansion, Taylor expansion
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ISSN:1674-1056
2058-3834
DOI:10.1088/1674-1056/19/1/010504