| 一类非线性偏微分方程的四阶格子Boltzmann模型 |
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| 引用本文： | 周志强,何郁波. 一类非线性偏微分方程的四阶格子Boltzmann模型[J]. 纯粹数学与应用数学, 2012, 28(1): 29-35. DOI: 10.3969/j.issn.1008-5513.2012.01.005 |
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| 作者姓名： | 周志强 何郁波 |
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| 作者单位： | 1.怀化学院数学系,湖南怀化,418008;2.怀化学院数学系,湖南怀化,418008 |
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| 基金项目： | 湖南省教育厅科研基金(07C505) |
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| 摘 要： | 通过Chapman-Enskog展开技术和多尺度分析,建立了一种新的D1Q4带修正项的四阶格子Boltzmann模型,一类非线性偏微分方程从连续的Boltzmann方程得到正确恢复．统一了KdV和Burgers等已知方程类型的格子BGK模型,还首次给出了组合KdV-Burgers,广义Burgers—Huxley等方程的四阶LBGK模型．数值模拟结果表明了该模型的有敢性和稳定性．
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| 关 键 词： | 非线性偏微分方程 格子Boltzmann模型 Chapman—Enskog多尺度展开 |
A fourth order lattice Boltzmann model for nonlinear partial differential equation |
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| Zhou Zhiqiang,He Yubo. A fourth order lattice Boltzmann model for nonlinear partial differential equation[J]. Pure and Applied Mathematics, 2012, 28(1): 29-35. DOI: 10.3969/j.issn.1008-5513.2012.01.005 |
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| Authors: | Zhou Zhiqiang He Yubo |
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| Affiliation: | (Department of Mathematics,Huaihua University,Huaihua 418008,China) |
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| Abstract: | A new D1Q4 fourth order lattice Boltzmann model with amending function is presented for nonlinear partial differential equations.By using Chapman-Enskog expansion technique and multiple-scale analysis,a class of NPEs are restored correctly from continuous Boltzmann equation.This paper not only gives a unified lattice BGK model for the well-known equation such as KdV and Burgers equation,but also firstly gives a fourth order LBGK model for the combined KdV-Burgers equation,generalized Burgers-Huxley equation,etc.Numerical simulation results show that the method described in this paper is effective and stable. |
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| Keywords: | nonlinear partial differential equations lattice Boltzmann model Chapman-Enskog expansion |
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