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In this paper, a kernel gradient corrected smoothed particle hydrodynamics (KGC-SPH) method is proposed to simulate the deformation process of a viscous liquid drop. The KGC-SPH method has higher accuracy and better stability than the SPH method, which is verified by simulating the stretching and rotating process of an isothermal viscous liquid drop, and the property of preservation of total angular momentum of the present method is also checked. And then, the formation of a stable spherical liquid drop based on van der Waals model is investigated, and a phenomenon of periodic oscillation with small amplitude is observed. Meanwhile, a new variable smoothing length is presented to remove the unstable phenomenon and a new surface tension technique is adopted in the simulation. Subsequently, the phenomenon of periodic oscillation of a van der Waals model liquid drop is simulated using KGC-SPH method, in which the influence of the elongation and Reynolds number on the amplitude and oscillation period is discussed.
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Keywords:
- SPH /
- viscous drop /
- van der Waals model /
- surface tension
[1] Zhang L, Zhang L F, Wu H Y, Wang J P 2009 Acta Phys. Sin. 58 703 (in Chinese)[张 亮、张立凤、吴海燕、王骥鹏 2009 58 703]
[2] Zhang A M, Yao X L, Li J 2008 Acta Phys. Sin. 57 1672 (in Chinese) [张阿漫、姚熊亮、李 佳 2008 57 1672]
[3] Zhang A M 2008 Chin. Phys. B 17 927
[4] Zhang A M, Yao X L 2008 Acta Phys. Sin. 57 339 (in Chinese) [张阿漫、姚熊亮 2008 57 339]
[5] Harlow F H 1957 Journal of the Association for Computing Machinery 4 137
[6] Zhao Y, Ji Z Z, Feng T 2004 Acta Phys. Sin. 53 671 (in Chinese) [赵 颖、季仲贞、冯 涛 2004 53 671]
[7] Zhong C W,Xie J F,Zhuo C S,Xiong S W, Yin D C 2009 Chin. Phys. B 18 4083
[8] Wang J F, Sun F X, Cheng R J 2010 Chin. Phys. B 19 060201
[9] Cheng R J,Cheng Y M, Ge H X 2009 Chin. Phys. B 18 4059
[10] Wang X D, Ouyang J, Su J 2010 Acta Phys. Sin. 59 6361(in Chinese) [王晓东、欧阳洁、苏 进 2010 59 6361]
[11] Gingold R A, Monaghan J J 1977 Mon. Not. R. Astron. Soc. 181 375
[12] Monaghan J J 1994 J. Comp. Phys. 110 399
[13] Morris J P, Fox P J, Zhu Y 1997 J. Comp. Phys. 136 214
[14] Watkins S J, Bhattal A S, Francis N, Turner J A, Whitworth A P 1996 Astron. Astrophys. Suppl. Ser. 119 177
[15] Nugent S, Posch H A 2000 Phys. Rev. E 62 4968
[16] Hu X Y, Adams N A 2006 J. Comp. Phys. 213 844
[17] Chen J K, Beraun J E 2000 Comp. Meth. Appl. Mech. Eng. 190 225
[18] Liu M B, Xie W P, Liu G R 2005 Appl. Math. Model. 29 1252
[19] Fang J, Parriaux A, Rentschler M, Ancey C 2009 Appl. Num. Math. 59 251
[20] Bonet J, Lok T S L 1999 Comput. Meth. Appl. Mech. Eng. 180 97
[21] Apfel R E, Tian Y, Jankovshy J, Shi T, Chen X, Holt R G, Trinh E, Croonquist A, Thornton K C, Sacco A, Jr, Coleman C, Leslie F W, Matthiesen D H 1997 Phys. Rev. Let. 78 1912
[22] Melean Y, Singalotti L D G, Hasmy A 2004 Comp. Phys. Comm. 157 191
[23] Lopez H, Sigalotti L D G 2006 Phys. Rev. E 73 051201-1
[24] Liu G R, Liu M B 2003 Smoothed Particle Hydrodynamics: A Mesh-free Particle Method (Singapore: World Scientific)
[25] Monaghan J J, Lattanzio J C 1985 Astron. Astrophys. 149 135
[26] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌、常建忠 2010 59 3654]
[27] Liu M B, Liu G R 2006 Appl. Num. Math. 56 19
[28] Silverman B W 1986 Statistics and Applied Probability (London: Chapman and Hall)
[29] Schussler M, Schmitt D 1981 Astron. Astrophys. 97 373
[30] Gray J P, Monaghan J J, Swift R P 2001 Comp. Meth. Appl. Mech. Eng. 190 6641
[31] Monaghan J J 2000 J. Comp. Phys. 159 290
[32] Tang B, Li J F, Wang T S 2008 Acta Phys. Sin. 57 6722 (in Chinese) [汤波、李俊峰、王天舒 2008 57 6722]
[33] Chang J Z, Liu M B, Liu H T 2008 Acta Phys. Sin. 57 3954 (in Chinese) [常建忠、刘谋斌、刘汉涛 2008 57 3954]
[34] Wang X L, Chen S 2010 Acta Phys. Sin. 59 6778 (in Chinese) [王晓亮、陈 硕 2010 59 6778]
[35] Trinh E, Wang T G 1982 J. Fluid Mech. 122 315
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[1] Zhang L, Zhang L F, Wu H Y, Wang J P 2009 Acta Phys. Sin. 58 703 (in Chinese)[张 亮、张立凤、吴海燕、王骥鹏 2009 58 703]
[2] Zhang A M, Yao X L, Li J 2008 Acta Phys. Sin. 57 1672 (in Chinese) [张阿漫、姚熊亮、李 佳 2008 57 1672]
[3] Zhang A M 2008 Chin. Phys. B 17 927
[4] Zhang A M, Yao X L 2008 Acta Phys. Sin. 57 339 (in Chinese) [张阿漫、姚熊亮 2008 57 339]
[5] Harlow F H 1957 Journal of the Association for Computing Machinery 4 137
[6] Zhao Y, Ji Z Z, Feng T 2004 Acta Phys. Sin. 53 671 (in Chinese) [赵 颖、季仲贞、冯 涛 2004 53 671]
[7] Zhong C W,Xie J F,Zhuo C S,Xiong S W, Yin D C 2009 Chin. Phys. B 18 4083
[8] Wang J F, Sun F X, Cheng R J 2010 Chin. Phys. B 19 060201
[9] Cheng R J,Cheng Y M, Ge H X 2009 Chin. Phys. B 18 4059
[10] Wang X D, Ouyang J, Su J 2010 Acta Phys. Sin. 59 6361(in Chinese) [王晓东、欧阳洁、苏 进 2010 59 6361]
[11] Gingold R A, Monaghan J J 1977 Mon. Not. R. Astron. Soc. 181 375
[12] Monaghan J J 1994 J. Comp. Phys. 110 399
[13] Morris J P, Fox P J, Zhu Y 1997 J. Comp. Phys. 136 214
[14] Watkins S J, Bhattal A S, Francis N, Turner J A, Whitworth A P 1996 Astron. Astrophys. Suppl. Ser. 119 177
[15] Nugent S, Posch H A 2000 Phys. Rev. E 62 4968
[16] Hu X Y, Adams N A 2006 J. Comp. Phys. 213 844
[17] Chen J K, Beraun J E 2000 Comp. Meth. Appl. Mech. Eng. 190 225
[18] Liu M B, Xie W P, Liu G R 2005 Appl. Math. Model. 29 1252
[19] Fang J, Parriaux A, Rentschler M, Ancey C 2009 Appl. Num. Math. 59 251
[20] Bonet J, Lok T S L 1999 Comput. Meth. Appl. Mech. Eng. 180 97
[21] Apfel R E, Tian Y, Jankovshy J, Shi T, Chen X, Holt R G, Trinh E, Croonquist A, Thornton K C, Sacco A, Jr, Coleman C, Leslie F W, Matthiesen D H 1997 Phys. Rev. Let. 78 1912
[22] Melean Y, Singalotti L D G, Hasmy A 2004 Comp. Phys. Comm. 157 191
[23] Lopez H, Sigalotti L D G 2006 Phys. Rev. E 73 051201-1
[24] Liu G R, Liu M B 2003 Smoothed Particle Hydrodynamics: A Mesh-free Particle Method (Singapore: World Scientific)
[25] Monaghan J J, Lattanzio J C 1985 Astron. Astrophys. 149 135
[26] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌、常建忠 2010 59 3654]
[27] Liu M B, Liu G R 2006 Appl. Num. Math. 56 19
[28] Silverman B W 1986 Statistics and Applied Probability (London: Chapman and Hall)
[29] Schussler M, Schmitt D 1981 Astron. Astrophys. 97 373
[30] Gray J P, Monaghan J J, Swift R P 2001 Comp. Meth. Appl. Mech. Eng. 190 6641
[31] Monaghan J J 2000 J. Comp. Phys. 159 290
[32] Tang B, Li J F, Wang T S 2008 Acta Phys. Sin. 57 6722 (in Chinese) [汤波、李俊峰、王天舒 2008 57 6722]
[33] Chang J Z, Liu M B, Liu H T 2008 Acta Phys. Sin. 57 3954 (in Chinese) [常建忠、刘谋斌、刘汉涛 2008 57 3954]
[34] Wang X L, Chen S 2010 Acta Phys. Sin. 59 6778 (in Chinese) [王晓亮、陈 硕 2010 59 6778]
[35] Trinh E, Wang T G 1982 J. Fluid Mech. 122 315
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