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应用基于投影算法的不可压缩光滑粒子动力学(incompressible smoothed particle hydrodynamics, ISPH)法对黏性液滴变形过程进行了数值仿真. 对于张力失稳导致的粒子非物理簇集问题, 采用粒子移位技术加以解决. 为了验证本文ISPH 算法的精度和稳定性, 分别模拟了圆形黏性液滴的拉伸变形过程以及方形液滴的旋转变形过程, 得到了不同时刻液滴内部的压力变化特征, 准确地捕捉了液滴自由面演化过程, 并将数值计算结果与文献中的解析解进行了比较.分析结果表明, 基于投影算法的不可压缩光滑粒子动力学方法结合粒子移位技术, 能够有效地模拟黏性液滴变形过程, 可以得到精确和稳定的结果.
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关键词:
- 不可压缩光滑粒子动力学 /
- 黏性液滴 /
- 自由面流动 /
- 数值仿真
A projection-based incompressible smooth particle hydrodynamics (ISPH) is applied to the simulation of the deformation process of viscous liquid drop. In our numerical computation, the particle shifting technique is used to overcome particle clustering due to the tensile instability in SPH. In order to verify the proposed ISPH, numerical simulations of a viscous circle drop stretching and a viscous square drop rotating are carried out. The pressure distribution in the drop is obtained, and the deformation process of viscous liquid drop is correctly captured. Comparisons between numerical results and the analytical solutions in the literature are presented. The simulation results show that the projection-based ISPH with particle shifting technique can be used to simulate the deformation process of viscous liquid drop with stability and accuracy.[1] Lucy L 1977 J. Astron. 82 12
[2] Gingold R A, Monaghan J J 1977 Mon. Not. R. Astron. Soc. 181 375
[3] Monaghan J J 1994 J. Comput. Phys. 110 339
[4] Qiu L C 2008 J. Hydraulic Eng. ASCE 134 5
[5] Jiang T, Ouyang J, Zhao X K, Ren J L 2011 Acta Phys. Sin. 60 054701 (in Chinese) [蒋涛, 欧阳洁, 赵晓凯, 任金莲 2011 物理学报 60 054701]
[6] Ma L Q, Liu M B, Chang J Z, Su T X, Liu H T 2012 Acta Phys. Sin. 61 244701 (in Chinese) [马理强, 刘谋斌, 常建忠, 苏铁熊, 刘汉涛 2012 物理学报 61 244701]
[7] Cummins S J, Rudman M 1999 J. Comput. Phys. 152 2
[8] Shao S and Lo E Y M 2003 Advances in Water Resources 26 7
[9] Lee E S, Moulinec C, Xu R, Violeau D, Laurence D, Stansby P 2008 J. Comput. Phys. 227 8417
[10] Monaghan J J, Lattanzio J 1985 Astronomy and Astrophysics 149 135
[11] Monaghan J J 1992 Annu. Rev. Astron. Astrophys. 30 543
[12] Van Der Vorst H A 1992 S. J. Sci. Stat. Comput. 13 631
[13] Monaghan J J 1989 J. Comput. Phys. 82 1
[14] Morris J P, Fox P J, Zhu Y 1997 J. Comput. Phys. 136 214
[15] Monaghan J J 2000 J. Comput. Phys. 159 290
[16] Xu R 2009 Ph. D. Dissertation (Manchester: University of Manchester)
[17] Colagrossi A 2005 Ph. D. Dissertation (Roma: Universitá di Roma La Sapienza)
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[1] Lucy L 1977 J. Astron. 82 12
[2] Gingold R A, Monaghan J J 1977 Mon. Not. R. Astron. Soc. 181 375
[3] Monaghan J J 1994 J. Comput. Phys. 110 339
[4] Qiu L C 2008 J. Hydraulic Eng. ASCE 134 5
[5] Jiang T, Ouyang J, Zhao X K, Ren J L 2011 Acta Phys. Sin. 60 054701 (in Chinese) [蒋涛, 欧阳洁, 赵晓凯, 任金莲 2011 物理学报 60 054701]
[6] Ma L Q, Liu M B, Chang J Z, Su T X, Liu H T 2012 Acta Phys. Sin. 61 244701 (in Chinese) [马理强, 刘谋斌, 常建忠, 苏铁熊, 刘汉涛 2012 物理学报 61 244701]
[7] Cummins S J, Rudman M 1999 J. Comput. Phys. 152 2
[8] Shao S and Lo E Y M 2003 Advances in Water Resources 26 7
[9] Lee E S, Moulinec C, Xu R, Violeau D, Laurence D, Stansby P 2008 J. Comput. Phys. 227 8417
[10] Monaghan J J, Lattanzio J 1985 Astronomy and Astrophysics 149 135
[11] Monaghan J J 1992 Annu. Rev. Astron. Astrophys. 30 543
[12] Van Der Vorst H A 1992 S. J. Sci. Stat. Comput. 13 631
[13] Monaghan J J 1989 J. Comput. Phys. 82 1
[14] Morris J P, Fox P J, Zhu Y 1997 J. Comput. Phys. 136 214
[15] Monaghan J J 2000 J. Comput. Phys. 159 290
[16] Xu R 2009 Ph. D. Dissertation (Manchester: University of Manchester)
[17] Colagrossi A 2005 Ph. D. Dissertation (Roma: Universitá di Roma La Sapienza)
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