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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.
[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 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 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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[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 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 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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