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In this paper, we present a modified smoothed particle hydrodynamics (SPH) method. The kernel approximation and the particle approximation are corrected to ensure that polynomial functions are exactly interpolated up to a given degree. Riemann solver is adopted to solve equations of fluid motion. A surface tension calculation program is used for considering the surface tension effects in droplets splashing. The process of droplet impact on liquid surface is numerically simulated by the modified smoothed particle hydrodynamics method. The numerical results clearly demonstrate that the modified SPH method can effectively describe the dynamics of droplet splashing and the variation of the free surface, and that the accuracy of the results can be stable.
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Keywords:
- droplet /
- smoothed particle hydrodynamics /
- surface tension /
- numerical simulation
[1] Harlow F H 1957 Methods Comput Phys. 3 319
[2] Harlow F H, Welch F J 1965 Phys Fluids 8 2182
[3] Hirt C W, Nichols D B 1981 J. Comput. Phys. 39 201
[4] M Sussman P, Smereka S, Osher A 1994 J Comput. Phys. 114146
[5] Liu G R, Liu M B 2003 Smoothed Particle Hydrodynamics: AMeshfree Particle Method (Singapore: World Scientific)
[6] Liu M B, Liu G R, Zong Z 2008 Int. J. Comput. Methods 5 135
[7] Monaghan J J 1994 J. Comput. Phys. 110 399
[8] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠 2010 59 3654]
[9] Colagrossi A, Landrini M 2003 J. Comput. Phys. 191 448
[10] Jiang T, Ouyang J, Zhao X K, Ren J L 2011 Acta Phys. Sin. 60054701 (in Chinese) [蒋涛,欧阳杰, 赵晓凯, 任金莲 2011 60 054701]
[11] Harlow F H, Shannon J P 1969 Appl. Phys. 38 3855
[12] Oguz Hasan N, Andrea P 1990 J. Fluid. Mech. 219 143
[13] Cai Y K 1989 Acta Mech. Sin. 21 273 (in Chinese) [蔡一坤 1989 力学学报 21 273]
[14] 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]
[15] Xu J 1999 Acta Scicentiarum Naturalum Universitis Pekinesis 3535 (in Chinese) [徐军 1999 北京大学学报(自然科学版) 35 35]
[16] Luo C X, Li H X, Chen T K, Chen S N 2002 J. Eng. Thermophys. 23 35 (in Chinese) [罗朝霞, 李会雄, 陈听宽, 陈善年 2002工程热 23 35]
[17] Zhang H, Hao Z W, Feng Z J 2008 J. Hydraulic Eng. 39 1316 (inChinese) [张华, 郝智文, 冯志军 2008 水利学报 39 1316]
[18] Chang J Z, Liu M B, Liu H T 2008 Acta Phys. Sin. 57 3954 (inChinese) [常建忠, 刘谋斌, 刘汉涛 2008 57 3954]
[19] Wendland H 1995 Adv. Comput. Math. 4 389
[20] Benz W 1990 Smooth Particle Hydrodynamics (Dordrecht:Kluwer Academinc Publishers) p269
[21] Morris J P 2000 Int. J. Numer. Meth. Fl. 33 333
[22] Wang X L, Chen S 2010 Acta Phys. Sin. 59 6778 (in Chinese) [王晓亮, 陈硕 2010 59 6778]
[23] Nugent S, Posch H A 2000 Phys. Rev. E 62 4968
[24] Zhang M Y, Zhang H, Zheng L L 2008 Heat. Mass. Transfer. 513410
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[1] Harlow F H 1957 Methods Comput Phys. 3 319
[2] Harlow F H, Welch F J 1965 Phys Fluids 8 2182
[3] Hirt C W, Nichols D B 1981 J. Comput. Phys. 39 201
[4] M Sussman P, Smereka S, Osher A 1994 J Comput. Phys. 114146
[5] Liu G R, Liu M B 2003 Smoothed Particle Hydrodynamics: AMeshfree Particle Method (Singapore: World Scientific)
[6] Liu M B, Liu G R, Zong Z 2008 Int. J. Comput. Methods 5 135
[7] Monaghan J J 1994 J. Comput. Phys. 110 399
[8] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠 2010 59 3654]
[9] Colagrossi A, Landrini M 2003 J. Comput. Phys. 191 448
[10] Jiang T, Ouyang J, Zhao X K, Ren J L 2011 Acta Phys. Sin. 60054701 (in Chinese) [蒋涛,欧阳杰, 赵晓凯, 任金莲 2011 60 054701]
[11] Harlow F H, Shannon J P 1969 Appl. Phys. 38 3855
[12] Oguz Hasan N, Andrea P 1990 J. Fluid. Mech. 219 143
[13] Cai Y K 1989 Acta Mech. Sin. 21 273 (in Chinese) [蔡一坤 1989 力学学报 21 273]
[14] 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]
[15] Xu J 1999 Acta Scicentiarum Naturalum Universitis Pekinesis 3535 (in Chinese) [徐军 1999 北京大学学报(自然科学版) 35 35]
[16] Luo C X, Li H X, Chen T K, Chen S N 2002 J. Eng. Thermophys. 23 35 (in Chinese) [罗朝霞, 李会雄, 陈听宽, 陈善年 2002工程热 23 35]
[17] Zhang H, Hao Z W, Feng Z J 2008 J. Hydraulic Eng. 39 1316 (inChinese) [张华, 郝智文, 冯志军 2008 水利学报 39 1316]
[18] Chang J Z, Liu M B, Liu H T 2008 Acta Phys. Sin. 57 3954 (inChinese) [常建忠, 刘谋斌, 刘汉涛 2008 57 3954]
[19] Wendland H 1995 Adv. Comput. Math. 4 389
[20] Benz W 1990 Smooth Particle Hydrodynamics (Dordrecht:Kluwer Academinc Publishers) p269
[21] Morris J P 2000 Int. J. Numer. Meth. Fl. 33 333
[22] Wang X L, Chen S 2010 Acta Phys. Sin. 59 6778 (in Chinese) [王晓亮, 陈硕 2010 59 6778]
[23] Nugent S, Posch H A 2000 Phys. Rev. E 62 4968
[24] Zhang M Y, Zhang H, Zheng L L 2008 Heat. Mass. Transfer. 513410
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