应用格子Boltzmann模型模拟一类二维偏微分方程

何郁波; 林晓艳; 董晓亮

doi:10.7498/aps.62.194701

摘要

针对一类含源的二维非线性偏微分方程, 通过Chapman-Enskog展开技术和多尺度分析提出了带修正项的简单格子Boltzmann模型. 用模型模拟了几类二维偏微分方程, 数值模拟结果与精确解相符合. 成功将格子Boltzmann方法应用到二维偏微分方程的数值求解中.

关键词:

For a class of two-dimensional nonlinear partial differential equation with the source term,a simple lattice Boltzmann model with amending function is proposed and studied using the Chapman-Enskog expansion technique and multiple-scale analysis. In this paper, some partial differential equation are simulated, the numerical results and exact solutions are shown to be almost completely fitting with each other. The lattice Boltzmann method is further extended to two-dimensional partial differential equation.

Keywords:

two-dimensional nonlinear partial differential equation /
lattice Boltzmann method /
Chapman-Enskog multi-scale expansion

作者及机构信息

1.
怀化学院数学系, 怀化 418008;

2.
北方民族大学信息与计算科学学院, 银川 750021

基金项目: 湖南省教育厅重点项目(批准号:08A503);湖南省教育厅青年骨干教师和国内访问学者基金(批准号:湘教通[2012]510号)资助的课题.

Authors and contacts

1.
Department of Mathematics, Huaihua University, Huaihua 418008, China;

2.
School of Information and Computation Science, The North University for Ethnics, Yinchuan 750021, China

Funds: Project supported by the Research Foundation of Education Bureau of Hunan Province, China (Grant No. 08A503), the Young Core Instructor and Domestic Visitor Foundation from the Education-Commission of Hunan Province, China (Grant No. [2012]510).

参考文献

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[2]	Fan E G 2000 Phys. Lett. A 277 212
[3]	Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[4]	Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
[5]	Ma S H, Fang J P, Zhu H P 2007 Acta Phys. Sin. 56 4319 (in Chinese) [马松华, 方建平, 朱海平 2007 物理学报 56 4339]
[6]	Liu Y P, Li Z B 2003 Chin. Phys. Lett. 20 317
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[8]	Zhu J M, Zheng C L, Ma Z Y 2004 Chin. Phys. 13 2008
[9]	Zhang T, Shi B C, Guo Z L, Chai Z H, Lu J H 2012 Phys. Rev. E 85 016701
[10]	Mao W, Guo Z L, Wang L 2013 Acta Phys. Sin. 62 084703 (in Chinese) [毛威, 郭照立, 王亮 2013 物理学报 62 084703]
[11]	Ma C F 2005 Chin. Phys. Lett. 22 02313
[12]	Ma C F, Tang J, Chen X H 2007 Chinese Journa L of Applied Mechanics 24 0519 (in Chinese) [马昌凤, 唐嘉, 陈小红 2007 应用力学学报 24 0519]
[13]	He Y B, Ma C F, Liang Q 2007 Acta Mathematicae Applicatae Sinica 30 1040 (in Chinese) [何郁波, 马昌凤, 梁茜 2007 应用数学学报 30 1040]
[14]	Lai H L, Ma C F 2009 Sci. China Ser. G 52 1053 (in Chinese) [赖惠林, 马昌凤 2009 中国科学: G辑 39 1053]
[15]	He Y B, Dong X L, Lin X Y 2012 Computer Engineering and Applications 48 038 (in Chinese) [何郁波, 董晓亮, 林晓艳 2012 计算机工程与应用 48 038]
[16]	Li B H, Fang H P 2004 Chin. Phys. 13 2087
[17]	Chen S Y, Fang H P 2004 Chin. Phys. 13 47
[18]	Shi B C, He N Z, Guo Z L 2004 Chin. Phys. 13 40
[19]	Lu D T, Liu Y,Xu Y S 2009 Chin. Phys. Lett. 26 034702
[20]	Sun D K, Xiang N, Chen K,Ni Z H 2013 Acta Phys. Sin. 62 024703 (in Chinese) [孙东科, 项楠, 陈科, 倪中华 2013 物理学报 62 024703]
[21]	Lai H L,Ma C F 2008 Journal of Fujian Normal University (Natural Sci. Edition) 24 015 (in Chinese) [赖惠林, 马昌凤 2008 福建师范大学学报 (自然科学版) 24 015]
[22]	Ruan H Y,Li H J 2006 Journal of Ningbo University (NSEE) 19 222 (in Chinese) [阮航宇, 李慧军 2006 宁波大学学报 (理工版) 19 222]

施引文献

[1]	Taogetusang, Bai Y M 2013 Acta Phys. Sin. 62 100201 (in Chinese) [套格图桑, 白玉梅 2013 物理学报 62 100201]
[2]	Fan E G 2000 Phys. Lett. A 277 212
[3]	Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[4]	Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
[5]	Ma S H, Fang J P, Zhu H P 2007 Acta Phys. Sin. 56 4319 (in Chinese) [马松华, 方建平, 朱海平 2007 物理学报 56 4339]
[6]	Liu Y P, Li Z B 2003 Chin. Phys. Lett. 20 317
[7]	Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 3246 (in Chinese) [套格图桑, 斯仁道尔吉 2006 物理学报 55 3246]
[8]	Zhu J M, Zheng C L, Ma Z Y 2004 Chin. Phys. 13 2008
[9]	Zhang T, Shi B C, Guo Z L, Chai Z H, Lu J H 2012 Phys. Rev. E 85 016701
[10]	Mao W, Guo Z L, Wang L 2013 Acta Phys. Sin. 62 084703 (in Chinese) [毛威, 郭照立, 王亮 2013 物理学报 62 084703]
[11]	Ma C F 2005 Chin. Phys. Lett. 22 02313
[12]	Ma C F, Tang J, Chen X H 2007 Chinese Journa L of Applied Mechanics 24 0519 (in Chinese) [马昌凤, 唐嘉, 陈小红 2007 应用力学学报 24 0519]
[13]	He Y B, Ma C F, Liang Q 2007 Acta Mathematicae Applicatae Sinica 30 1040 (in Chinese) [何郁波, 马昌凤, 梁茜 2007 应用数学学报 30 1040]
[14]	Lai H L, Ma C F 2009 Sci. China Ser. G 52 1053 (in Chinese) [赖惠林, 马昌凤 2009 中国科学: G辑 39 1053]
[15]	He Y B, Dong X L, Lin X Y 2012 Computer Engineering and Applications 48 038 (in Chinese) [何郁波, 董晓亮, 林晓艳 2012 计算机工程与应用 48 038]
[16]	Li B H, Fang H P 2004 Chin. Phys. 13 2087
[17]	Chen S Y, Fang H P 2004 Chin. Phys. 13 47
[18]	Shi B C, He N Z, Guo Z L 2004 Chin. Phys. 13 40
[19]	Lu D T, Liu Y,Xu Y S 2009 Chin. Phys. Lett. 26 034702
[20]	Sun D K, Xiang N, Chen K,Ni Z H 2013 Acta Phys. Sin. 62 024703 (in Chinese) [孙东科, 项楠, 陈科, 倪中华 2013 物理学报 62 024703]
[21]	Lai H L,Ma C F 2008 Journal of Fujian Normal University (Natural Sci. Edition) 24 015 (in Chinese) [赖惠林, 马昌凤 2008 福建师范大学学报 (自然科学版) 24 015]
[22]	Ruan H Y,Li H J 2006 Journal of Ningbo University (NSEE) 19 222 (in Chinese) [阮航宇, 李慧军 2006 宁波大学学报 (理工版) 19 222]

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