Modeling of the New Boundary of Reaction Force Based on Particle Collision in the Smoothed Particle Hydrodynamics

Document Type : Original Article


1 School of Energy and Power Engineering, Jiangsu University of Science and Technology, Zhenjiang Jiangsu 212003, China

2 School of Mathematics and Information Engineering, Lianyungang Normal College, Lianyungang 222006, China


A new reaction force model of particle collision is built, which is based on the conservation of momentum and the conservation of energy. Combined with weakly compressible smoothed particle hydrodynamics and the artificial compressibility, the new model and a conventional reaction force model of Lennard-Jones is used to simulate the phenomenon of shear driven cavity and the flow around a square cylinder, respectively. For verifying the accuracy of the new model, the DNS method is also used to simulate the flow phenomenon. By comparing and analyzing the calculating results, it can be concluded that: The new reaction force model can effectively prevent particles from unphysically penetrating through the boundary, and the variation of velocity and tangential stress near the boundary can be relatively accurate calculated. The new model helps to enhance the calculation accuracy of smooth particle hydrodynamics (SPH) for the whole flow field, and it has relatively good stability.


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[1]     Daxini SD, Prajapati JM. A Review on Recent Contribution of Meshfree Methods to Structure and Fracture Mechanics Applications. Sci World J 2014;2014:1–13. doi:10.1155/2014/247172.
[2]     Lucy LB. A numerical approach to the testing of the fission hypothesis. Astron J 1977;82:1013. doi:10.1086/112164.
[3]     Gingold RA, Monaghan JJ. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 1977;181:375–89. doi:10.1093/mnras/181.3.375.
[4]     Altomare C, Crespo AJC, Domínguez JM, Gómez-Gesteira M, Suzuki T, Verwaest T. Applicability of Smoothed Particle Hydrodynamics for estimation of sea wave impact on coastal structures. Coast Eng 2015;96:1–12. doi:10.1016/j.coastaleng.2014.11.001.
[5]     Soutter J, Hamilton N, Russell P, Russell C, Bushby K, Sloper P, et al. The Golden Freeway: a preliminary evaluation of a pilot study advancing information technology as a social intervention for boys with Duchenne muscular dystrophy and their families. Heal Soc Care Community 2004;12:25–33. doi:10.1111/j.1365-2524.2004.00465.x.
[6]     Nguyen MT, Aly AM, Lee S-W. A numerical study on unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies using the ISPH method. Int J Numer Methods Heat Fluid Flow 2018;28:684–703. doi:10.1108/HFF-02-2017-0058.
[7]     Aly AM. Modeling of multi-phase flows and natural convection in a square cavity using an incompressible smoothed particle hydrodynamics. Int J Numer Methods Heat Fluid Flow 2015;25:513–33. doi:10.1108/HFF-05-2014-0161.
[8]     Basser H, Rudman M, Daly E. SPH modelling of multi-fluid lock-exchange over and within porous media. Adv Water Resour 2017;108:15–28. doi:10.1016/j.advwatres.2017.07.011.
[9]     Kunz P, Zarikos IM, Karadimitriou NK, Huber M, Nieken U, Hassanizadeh SM. Study of Multi-phase Flow in Porous Media: Comparison of SPH Simulations with Micro-model Experiments. Transp Porous Media 2016;114:581–600. doi:10.1007/s11242-015-0599-1.
[10]   Mayrhofer A, Laurence D, Rogers BD, Violeau D. DNS and LES of 3-D wall-bounded turbulence using Smoothed Particle Hydrodynamics. Comput Fluids 2015;115:86–97. doi:10.1016/j.compfluid.2015.03.029.
[11]   Di Mascio A, Antuono M, Colagrossi A, Marrone S. Smoothed particle hydrodynamics method from a large eddy simulation perspective. Phys Fluids 2017;29:035102. doi:10.1063/1.4978274.
[12]   Ni W, Lu L, Fang J, Moulinec C, Yao Y. Direct numerical simulation of turbulent channel flow with spanwise alternatively distributed strips control. Mod Phys Lett B 2018;32:1840004. doi:10.1142/S0217984918400043.
[13]   Liu, G. R. and Liu, M. B., Smoothed Particle Hydrodynamics: A meshfree particle method, Word Scientific Publishing Co, Pte. Ltd. 2003.
[14]   Monaghan JJ. Simulating Free Surface Flows with SPH. J Comput Phys 1994;110:399–406. doi:10.1006/jcph.1994.1034.
[16]   Hong-Fu HY-WQ, Wei-Ran ZJ-LG. A new repulsive model for solid boundary condition in smoothed particle hydrodynamics [J]. Acta Phys Sin 2013;4.
[17]   Cummins SJ, Rudman M. An SPH Projection Method. J Comput Phys 1999;152:584–607. doi:10.1006/jcph.1999.6246.
[18]   Dalrymple RA, Knio O. SPH Modelling of Water Waves. Coast. Dyn. ’01, Reston, VA: American Society of Civil Engineers; 2001, p. 779–87. doi:10.1061/40566(260)80.
[19]   LIU MB, LIU GR, ZONG Z. AN OVERVIEW ON SMOOTHED PARTICLE HYDRODYNAMICS. Int J Comput Methods 2008;05:135–88. doi:10.1142/S021987620800142X.
[20]   Morris JP. Analysis of smoothed particle hydrodynamics with applications. Monash University Australia; 1996.
[21]   Lee E-S, Moulinec C, Xu R, Violeau D, Laurence D, Stansby P. Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method. J Comput Phys 2008;227:8417–36. doi:10.1016/
[22]   Morris JP, Fox PJ, Zhu Y. Modeling Low Reynolds Number Incompressible Flows Using SPH. J Comput Phys 1997;136:214–26. doi:10.1006/jcph.1997.5776.