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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.
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Keywords:
- two-dimensional nonlinear partial differential equation /
- lattice Boltzmann method /
- Chapman-Enskog multi-scale expansion
[1] Taogetusang, Bai Y M 2013 Acta Phys. Sin. 62 100201 (in Chinese) [套格图桑, 白玉梅 2013 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 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 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 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 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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[1] Taogetusang, Bai Y M 2013 Acta Phys. Sin. 62 100201 (in Chinese) [套格图桑, 白玉梅 2013 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 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 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 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 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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