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耦合不可压流场输运方程的格子Boltzmann方法研究

苏进 欧阳洁 王晓东

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耦合不可压流场输运方程的格子Boltzmann方法研究

苏进, 欧阳洁, 王晓东

Lattice Boltzmann method for an advective transport equation coupled with incompressible flow field

Su Jin, Ouyang Jie, Wang Xiao-Dong
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  • 基于格子Boltzmann方法,提出了求解耦合不可压缩流场输运方程的一种改进数值方法. 该方法使用格子Boltzmann方法求解流场方程,并根据流场格子模型的密度分布函数构建了输运方程的二阶离散格式. 通过二维平板通道流场输运系统验证了该方法的有效性.数值结果表明,该方法可以有效地减少计算过程中出现的非物理耗散, 并克服了传统模型所需巨大存储量的缺点.
    In this paper, an improved numerical scheme based on the lattice BGK method (LBM) is proposed for solving the advective transport equation coupled with an incompressible flow. We utilize the LBM to solve the equations of flow field and build a second order discrete scheme for the advective transport equations using the probability density function of LBM. Meanwhile, the validity of the method is verified by an advective transport in a planar channel flow. Numerical results show that the method reduces the numerical dissipation efficiently and it involves consistently smaller memory requirements compared with previous studies.
    • 基金项目: 国家重点基础研究发展计划(批准号: 2012CB025903)和国家自然科学基金(批准号: 10871159)资助的课题.
    • Funds: Project supported by the National Basic Research Program of China (Grant No. 2012CB025903) and the National Natural Science Foundation of China (Grant No. 10871159).
    [1]

    Larson R G 1999 The Structure and Rheology of Complex Fluid (New York: Oxford University Press) p156

    [2]

    Wu Q Y, Wu J A 2002 Polymer Rheology (Beijing: Higher Education Press) p78 (in Chinese) [吴其晔, 巫静安 2002 高分子材料流变学(北京:高等教育出版社) 第78页]

    [3]

    Beris A N, Edwards B J 1999 Rheol. Acta 38 117

    [4]

    Bhave A V, Menon A K, Armstrong R C, Brown R A 1993 J. Rheol. 37 413

    [5]

    Guo Z L, Zhen C G 2008 Theory and Applications of Lattice Boltzmann Method (Beijing: Science Press) p77 (in Chinese) [郭照立, 郑楚光 2008 流体动力学的格子Boltzmann方法 (北京:科学出版社) 第77页]

    [6]

    Bhatnagar J, Gross E P, Krook M K 1954 Phys. Rev. 94 511

    [7]

    Zeng J B, Li L J, Liao Q, Chen Q H, Cui W Z, Pan L M 2010 Acta Phys. Sin. 59 178 (in Chinese) [曾建邦, 李隆键, 廖全, 陈清华, 崔文智, 潘良明 2010 物理学报 59 178]

    [8]

    Shi Z Y, Hu G H , Zhou Z W 2010 Acta Phys. Sin. 59 2595 (in Chinese) [石自媛, 胡国辉, 周哲玮 2010 物理学报 59 2595]

    [9]

    Denniston C, Orlandini E, Yeomans J M 2001 Phys. Rev. E 63 056702

    [10]

    Marenduzzo D, Orlandini E, Cates M E, Yeomans J M 2007 Phys. Rev. E 76 031921

    [11]

    Henrich O, Marenduzzo D, Stratford K, Cates M E 2009 Comput. Math. Appl. 8 47

    [12]

    Alexander K 2005 Ph. D. Dissertation (Yale: Yale University)

    [13]

    Guo Z L, Shi B C, Wang N C 2000 J. Comput. Phys. 165 288

  • [1]

    Larson R G 1999 The Structure and Rheology of Complex Fluid (New York: Oxford University Press) p156

    [2]

    Wu Q Y, Wu J A 2002 Polymer Rheology (Beijing: Higher Education Press) p78 (in Chinese) [吴其晔, 巫静安 2002 高分子材料流变学(北京:高等教育出版社) 第78页]

    [3]

    Beris A N, Edwards B J 1999 Rheol. Acta 38 117

    [4]

    Bhave A V, Menon A K, Armstrong R C, Brown R A 1993 J. Rheol. 37 413

    [5]

    Guo Z L, Zhen C G 2008 Theory and Applications of Lattice Boltzmann Method (Beijing: Science Press) p77 (in Chinese) [郭照立, 郑楚光 2008 流体动力学的格子Boltzmann方法 (北京:科学出版社) 第77页]

    [6]

    Bhatnagar J, Gross E P, Krook M K 1954 Phys. Rev. 94 511

    [7]

    Zeng J B, Li L J, Liao Q, Chen Q H, Cui W Z, Pan L M 2010 Acta Phys. Sin. 59 178 (in Chinese) [曾建邦, 李隆键, 廖全, 陈清华, 崔文智, 潘良明 2010 物理学报 59 178]

    [8]

    Shi Z Y, Hu G H , Zhou Z W 2010 Acta Phys. Sin. 59 2595 (in Chinese) [石自媛, 胡国辉, 周哲玮 2010 物理学报 59 2595]

    [9]

    Denniston C, Orlandini E, Yeomans J M 2001 Phys. Rev. E 63 056702

    [10]

    Marenduzzo D, Orlandini E, Cates M E, Yeomans J M 2007 Phys. Rev. E 76 031921

    [11]

    Henrich O, Marenduzzo D, Stratford K, Cates M E 2009 Comput. Math. Appl. 8 47

    [12]

    Alexander K 2005 Ph. D. Dissertation (Yale: Yale University)

    [13]

    Guo Z L, Shi B C, Wang N C 2000 J. Comput. Phys. 165 288

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  • 被引次数: 0
出版历程
  • 收稿日期:  2011-05-04
  • 修回日期:  2012-05-28
  • 刊出日期:  2012-05-05

耦合不可压流场输运方程的格子Boltzmann方法研究

  • 1. 西北工业大学应用数学系, 西安 710129
    基金项目: 国家重点基础研究发展计划(批准号: 2012CB025903)和国家自然科学基金(批准号: 10871159)资助的课题.

摘要: 基于格子Boltzmann方法,提出了求解耦合不可压缩流场输运方程的一种改进数值方法. 该方法使用格子Boltzmann方法求解流场方程,并根据流场格子模型的密度分布函数构建了输运方程的二阶离散格式. 通过二维平板通道流场输运系统验证了该方法的有效性.数值结果表明,该方法可以有效地减少计算过程中出现的非物理耗散, 并克服了传统模型所需巨大存储量的缺点.

English Abstract

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