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由于Lagrange粒子法的本质, 固壁边界条件的施加一直是光滑粒子动力学方法的难点之一. 本文从固壁边界的物理原理出发, 应用多层虚粒子表征固壁边界, 提出了一种新型固壁边界施加模型. 将虚粒子看作流体的扩展, 计算中虚粒子密度保持不变, 压力、速度等参数通过对流体粒子的插值获得, 虚粒子有条件的参与控制方程的计算, 对流体的密度/压力产生影响, 通过压力梯度隐式地表征壁面与流体之间的作用强度并对流体粒子施加沿壁面法线方向的斥力作用, 防止流体粒子对壁面的穿透. 数值算例测试结果表明, 与现有固壁边界施加方法相比, 本文方法更加符合流体与固壁边界作用的物理原理, 可以简单、有效地施加固壁边界条件, 方便地应用于具有复杂几何边界的问题, 获得稳定的流场形态、规则的粒子秩序及良好的速度、压力等参量的分布.As the smoothed particle hydrodynamics (SPH) is a truly Lagrangian meshfree method, the implementation of solid boundary condition has been one of the key problems that hinder SPH from applying to lots of engineering problems. In order to treat the boundary conditions efficiently, based on the boundary-fluid interaction principles, a new boundary treatment method is proposed. In this method, the solid boundary is repreflented implicitly by several layers of dummy particles along the boundary line. During the simulation, the dummy particles are treated as an extension of the fluid phase. The densities of dummy particles are kept constant, and the pressures and velocities are interpolated from the nearby fluid particles at each time step. Dummy particles can be involved in the calculation of the continuity equation conditionally and exert influences on the density/pressure field of the fluid phase. Then, for the fluid particles that approach the solid boundary, local pressure gradients are used to repreflent the dummy-fluid particle pair’s interaction strength and act as the boundary force term implicitly, which is tuned to be repulsive only and normal to the boundary. Thus, large pressure gradients mean strong boundary-fluid interaction strength, and the boundary force from the dummy particles should also be large enough to preflent the fluid particles from penetrating the solid boundary; and on the contrary, small pressure gradients mean weak boundary-fluid interaction strength and the boundary force becomes soft and little disturbs the flow field. Results of numerical tests demonstrate that, compared with the existing boundary treatment methods, the new method is in better accordance with the physical principles of the fluid-boundary interaction, and is able to treat arbitrary solid boundaries with limited modeling and computational costs. With the help of this new boundary treatment method, the stable flow field, well-ordered particle distribution, smooth velocity and pressure fields could be obtained. Theoretically, this new boundary treatment method could be directly used in three-dimensional multi-phase problems. Further tests are planned to be carried out; meanwhile, expanding the new boundary treatment method to rigid-fluid interaction problems is also a work in the future.
[1] Lucy L B 1977 Astron. J. 82 1013
[2] Gingold R A, Monaghan J J 1977 Mon. Not. R. Astron. Soc. 181 375
[3] Zhang A M 2008 Chin. Phys. B 22 927
[4] Sun Z H, Han R J 2008 Chin. Phys. B 17 3185
[5] Qiang H F, Shi C, Chen F Z, Han Y W 2013 Acta Phys. Sin. 62 214701 (in Chinese) [强洪夫, 石超, 陈福振, 韩亚伟 2013 物理学报 62 214701]
[6] Monaghan J J 2005 Rep. Prog. Phys. 68 1703
[7] Monaghan J J 1994 J. Comput. Phys. 110 399
[8] Monaghan J J, Kajtar J B 2009 Comput. Phys. Commun. 180 1811
[9] Liu M B, Shao J R, Chang J Z 2012 Sci. China Technol. Sc. 55 244
[10] Han Y W, Qiang H F, Zhao J L, Gao W R 2013 Acta Phys. Sin. 62 044702 (in Chinese) [韩亚伟, 强洪夫, 赵玖玲, 高巍然 2013 物理学报 62 044702]
[11] Han Y W, Qiang H F, Wang K P, Gao W R 2011 Eng. Mech. 28 245 (in Chinese) [强洪夫, 韩亚伟, 王坤鹏, 高巍然 2011 工程力学 28 245]
[12] Morris J P, Fox P J, Zhu Y 1997 J. Comput. Phys. 136 214
[13] Liu M B, Liu G R, Lam K Y 2002 Shock Waves 12 181
[14] Colagrossi A, Landrini M 2003 J. Comput. Phys. 191 448
[15] Colagrossi A, Lugni C, Brocchini M 2010 J. Hydraul. Res. 48 94
[16] Marrone S, Antuono M, Colagrossi A, Colicchio G, Touzé D L, Graziani G 2011 Comput. Methods Appl. Mech. Engrg. 200 1526
[17] Adami S, Hu X Y, Adams N A 2012 J. Comput. Phys. 231 7057
[18] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠 2010 物理学报 59 3654]
[19] Liu G R, Liu M B (translate by Han X, Yang G, Qiang H F) 2005 Smoothed Particle Hydrodynamics: A Meshfree Particle Method (Changsha: Hunan University Press) pp58-67 (in Chinese) [Liu G R, Liu M B (韩旭, 杨刚, 强洪夫 译) 2005 光滑粒子流体动力学-一种无网格粒子法 (长沙:湖南大学出版社)第58-67页]
[20] Bonet J, Lok T S L 1999 Comput. Method. Appl. M. 180 97
[21] Marrone S, Bouscasse B, Colagrossi A, Antuono M 2012 Comput. Fluids 69 54
[22] Chen J K, Beraun J E, Carney T C 1999 Int. J. Numer. Meth. Eng. 46 231
[23] Schmid M, Klein F 1995 NADCA 18. International Die Casting Congress and Exposition, Indianapolis, 1995, p93
[24] He Y 2012 M.S. Thesis (Guangzhou: South China University of Technology) (in Chinese) [何毅 2012 硕士学位论文 (广州: 华南理工大学)]
[25] Cleary P W, Ha J 2000 Int. J. Cast Metal. Res. 12 409
[26] Koshizuka S, Oka Y 1996 Nucl. Sci. Eng. 123 421
[27] Lobovsky L, Botia-Vera E, Castellana F, Mas-Soler J, Souto-Iglesias A 2014 J. Fluid. Struct. 48 407
[28] Monaghan J J 2012 Annu. Rev. Fluid Mech. 44 323
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[1] Lucy L B 1977 Astron. J. 82 1013
[2] Gingold R A, Monaghan J J 1977 Mon. Not. R. Astron. Soc. 181 375
[3] Zhang A M 2008 Chin. Phys. B 22 927
[4] Sun Z H, Han R J 2008 Chin. Phys. B 17 3185
[5] Qiang H F, Shi C, Chen F Z, Han Y W 2013 Acta Phys. Sin. 62 214701 (in Chinese) [强洪夫, 石超, 陈福振, 韩亚伟 2013 物理学报 62 214701]
[6] Monaghan J J 2005 Rep. Prog. Phys. 68 1703
[7] Monaghan J J 1994 J. Comput. Phys. 110 399
[8] Monaghan J J, Kajtar J B 2009 Comput. Phys. Commun. 180 1811
[9] Liu M B, Shao J R, Chang J Z 2012 Sci. China Technol. Sc. 55 244
[10] Han Y W, Qiang H F, Zhao J L, Gao W R 2013 Acta Phys. Sin. 62 044702 (in Chinese) [韩亚伟, 强洪夫, 赵玖玲, 高巍然 2013 物理学报 62 044702]
[11] Han Y W, Qiang H F, Wang K P, Gao W R 2011 Eng. Mech. 28 245 (in Chinese) [强洪夫, 韩亚伟, 王坤鹏, 高巍然 2011 工程力学 28 245]
[12] Morris J P, Fox P J, Zhu Y 1997 J. Comput. Phys. 136 214
[13] Liu M B, Liu G R, Lam K Y 2002 Shock Waves 12 181
[14] Colagrossi A, Landrini M 2003 J. Comput. Phys. 191 448
[15] Colagrossi A, Lugni C, Brocchini M 2010 J. Hydraul. Res. 48 94
[16] Marrone S, Antuono M, Colagrossi A, Colicchio G, Touzé D L, Graziani G 2011 Comput. Methods Appl. Mech. Engrg. 200 1526
[17] Adami S, Hu X Y, Adams N A 2012 J. Comput. Phys. 231 7057
[18] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠 2010 物理学报 59 3654]
[19] Liu G R, Liu M B (translate by Han X, Yang G, Qiang H F) 2005 Smoothed Particle Hydrodynamics: A Meshfree Particle Method (Changsha: Hunan University Press) pp58-67 (in Chinese) [Liu G R, Liu M B (韩旭, 杨刚, 强洪夫 译) 2005 光滑粒子流体动力学-一种无网格粒子法 (长沙:湖南大学出版社)第58-67页]
[20] Bonet J, Lok T S L 1999 Comput. Method. Appl. M. 180 97
[21] Marrone S, Bouscasse B, Colagrossi A, Antuono M 2012 Comput. Fluids 69 54
[22] Chen J K, Beraun J E, Carney T C 1999 Int. J. Numer. Meth. Eng. 46 231
[23] Schmid M, Klein F 1995 NADCA 18. International Die Casting Congress and Exposition, Indianapolis, 1995, p93
[24] He Y 2012 M.S. Thesis (Guangzhou: South China University of Technology) (in Chinese) [何毅 2012 硕士学位论文 (广州: 华南理工大学)]
[25] Cleary P W, Ha J 2000 Int. J. Cast Metal. Res. 12 409
[26] Koshizuka S, Oka Y 1996 Nucl. Sci. Eng. 123 421
[27] Lobovsky L, Botia-Vera E, Castellana F, Mas-Soler J, Souto-Iglesias A 2014 J. Fluid. Struct. 48 407
[28] Monaghan J J 2012 Annu. Rev. Fluid Mech. 44 323
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