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An Investigation into Neighbouring Search Techniques in Meshfree Particle Methods: An Evaluation of the Neighbour Lists and the Direct Search

  • C. A. D. Fraga FilhoEmail author
  • L. L. Schuina
  • B. S. Porto
Original Paper
  • 93 Downloads

Abstract

Meshfree particle methods are being increasingly employed in solving problems in automotive, aeronautics and oil industries, environmental and geophysical problems, biomechanics and medicine, hydraulic erosion, sediment transport, physics and astronomy, among other areas. Regardless of the application of the particle method, the search for neighbour particles must be done at each numerical iteration (especially in dynamic cases). In 2-D studies, the neighbour lists (linked and Verlet) are techniques commonly used in simulations. This paper presents an investigation of the computational efficiency of the linked list technique through comparison with results of simulations of the direct search (the simplest neighbour search technique). Different numbers of particles and interpolation functions have been used in the tests. By using a simple matrix in the storage of neighbour particles, an improvement in the computational efficiency (in comparison with the direct search’s time processing) has not been seen when the linked list algorithm has been utilised. A similar performance between linked list and direct search has been achieved when the neighbour particles have been stored in pairs (even though the cell-linked list has been updated at each numerical iteration). From the analyses of the CPU processing times found in the problems simulated in this work, in which the efficiency of the linked list was only similar to the direct search, it was concluded that is necessary the implementation of a optimisation technique for computational time saving. The Verlet list is a linked list optimisation proposal in which the neighbour list is not update at each numerical iteration. Through an appropriate choice of the cutoff radius, it is ensured that there is no loss in accuracy in the location of neighbouring particles. Optimisation attempts using the Verlet list have been performed but the improvement in the computational efficiency are not satisfactory in all cases.

Notes

Compliance with Ethical Standards

Conflict of interest

The authors certify that they have no affiliation with or involvement in any organization or entity with any financial or non-financial interest in the subject matter or materials discussed in this manuscript.

References

  1. 1.
    Li S, Liu WK (2002) Meshfree and particle methods and their applications. Appl Mech Rev 55(1):1–34.  https://doi.org/10.1115/1.1431547 CrossRefGoogle Scholar
  2. 2.
    Huerta A, Belytschko T, Fernandez-Méndez S, Rabczuk T (2004) Meshfree methods. Encyclopedia of computational mechanics. Wiley, New YorkGoogle Scholar
  3. 3.
    Idelsohn SR, Oñate E, Becker P (2018) Particle methods in computational fluid dynamics. In: Stein E, de Borst R, Hughes TJR (eds) Encyclopedia of computational mechanics, 2nd edn. Wiley, Chichester, pp 1–41Google Scholar
  4. 4.
    Onderik J, Ďurikovič R (2007) Efficient neighbor search for particle-based fluids. J Appl Math Stat Inform (JAMSI), 2(3). http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.105.6732&rep=rep1&type=pdf. Accessed 19 April 2019
  5. 5.
    Fraga Filho CAD (2019) Smoothed particle hydrodynamics: fundamentals and basic applications in continuum mechanics. Springer Nature, BaselCrossRefGoogle Scholar
  6. 6.
    Olliff J, Alford B, Simkins DC Jr (2018) Efficient searching in meshfree methods. Comput Mech 62(6):1461–1483.  https://doi.org/10.1007/s00466-018-1574-9 MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Koshizuka S, Nobe A, Oka Y (1998) Numerical analysis of breaking waves using the moving particle semi-implicit method. Int J Numer Methods Fluids 26(7):751–769.  https://doi.org/10.1002/(SICI)1097-0363(19980415)26:7%3c751:AID-FLD671%3e3.0.CO;2-C CrossRefzbMATHGoogle Scholar
  8. 8.
    Slattery SR, Hamilton SP, Evans TM (2015) A modified moving least square algorithm for solution transfer on a spacer grid surface. In: Proceedings of ANS AMC2015—join international conference in mathematics and computation, Nashville, Tenessee, 2015. https://www.casl.gov/sites/default/files/docs/CASL-U-2015-0177-000.pdf. Accessed 19 April 2019
  9. 9.
    Jun S, Liu WK, Belytschko T (1998) Explicit reproducing kernel particle methods for large deformation problems. Int J Numer Methods Eng 41(1):137–166.  https://doi.org/10.1002/(SICI)1097-0207(19980115)41:1%3c137:AID-NME280%3e3.0.CO;2-A CrossRefzbMATHGoogle Scholar
  10. 10.
    Wu N, Chen BS, Tsay T (2014) A review on the modified finite point method. Math Probl Eng 1–29:2014.  https://doi.org/10.1155/2014/350364 MathSciNetGoogle Scholar
  11. 11.
    Samuel H (2018) A deformable particle-in-cell method for advective transport in geodynamic modelling. Geophys J Int 214(3):1744–1773.  https://doi.org/10.1093/gji/ggy231 CrossRefGoogle Scholar
  12. 12.
    Wang D, Hsiao F, Chuang C, Lee Y (2007) Algorithm optimization in molecular dynamics simulation. Comput Phys Commun 177(7):551–559.  https://doi.org/10.1016/j.cpc.2007.05.009 MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Howard MP, Anderson JA, Nikoubashmana A, Glotzerb SC, Panagiotopoulos AZ (2016) Efficient neighbor list calculation for molecular simulation of colloidal systems using graphics processing units. Comput Phys Commun 203:45–52.  https://doi.org/10.1016/j.cpc.2016.02.003 CrossRefGoogle Scholar
  14. 14.
    Oñate E, Idelsohn SR, Del Pin F, Aubry R (2004) The particle finite element method. An overview. Int J Computat Methods 1(2):267–307.  https://doi.org/10.1142/s0219876204000204 CrossRefzbMATHGoogle Scholar
  15. 15.
    Domínguez JM, Crespo AJC, Gómez-Gesteira M, Marongiu JC (2011) Neighbour lists in smoothed particle hydrodynamics. Int J Numer Methods Fluids 67(12):2026–2042.  https://doi.org/10.1002/fld.2481 MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Viccione G, Bovolin V, Carratelli EP (2008) Defining and optimizing algorithms for neighbouring particle identification in SPH fluid simulations. Int J Numer Methods Fluids 58(6):625–638.  https://doi.org/10.1002/fld.1761 CrossRefzbMATHGoogle Scholar
  17. 17.
    Winchenbach R, Hochstetter H, Kolb A (2016) Constrained neighbor lists for SPH-based fluid simulations. In: Proceedings of eurographics/ACM SIGGRAPH symposium on computer animation, pp 49–56, Zurich, Switzerland, 2016. https://pdfs.semanticscholar.org/a7ef/0a369943a4cf616d96ccc85480de07606e69.pdf. Accessed 19 April 2019
  18. 18.
    Liu GR, Liu MB (2003) Smoothed particle hydrodynamics: a meshfree particle method. World Scientific, SingaporeCrossRefzbMATHGoogle Scholar
  19. 19.
    Rajasekaran S, Reif J (2007) Handbook of parallel computing: models, algorithms and applications. Chapmann and Hall/CRC, Boca RatonCrossRefzbMATHGoogle Scholar
  20. 20.
    Jahanbakhsh E, Pacot O, Avellan F (2012) Implementation of a parallel SPH-FPM solver for fluid flows. Zetta Numer Simul Sci Technol 1:16–20Google Scholar
  21. 21.
    Shadloo MS, Oger G, Le Touzé D (2016) Smoothed particle hydrodynamics method for fluid flows, towards industrial applications: motivations, current state, and challenges. Comput Fluids 136(10):11–34.  https://doi.org/10.1016/j.compfluid.2016.05.029 MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Leroy A (2014) Un nouveau modèle SPH incompressible: vers l’application à des cas industriels. Ph.D. Thesis, Université Paris-Est, France, 2014. http://www.theses.fr/2014PEST1065. Accessed 20 July 2018
  23. 23.
    Smojvera I, Ivančevića D (2017) Application of numerical methods in the improvement of safety of aeronautical structures. Transport Res Procedia 28:164–172.  https://doi.org/10.1016/j.trpro.2017.12.182 CrossRefGoogle Scholar
  24. 24.
    Koshizuka S (2012) Current achievements and future perspectives on particle simulation technologies for fluid dynamics and heat transfer. J Nucl Sci Technol 48(2):155–168.  https://doi.org/10.1080/18811248.2011.9711690 MathSciNetCrossRefGoogle Scholar
  25. 25.
    Cleary P, Joseph H, Vladimir A, Nguyen T (2002) Flow modelling in casting processes. Appl Math Model 26(2):171–190.  https://doi.org/10.1016/S0307-904X(01)00054-3 CrossRefzbMATHGoogle Scholar
  26. 26.
    Cleary PW, Savage G, Ha J, Prakash M (2014) Flow analysis and validation of numerical modelling for a thin walled high pressure die casting using SPH. Computat Particle Mech 1(3):229–243.  https://doi.org/10.1007/s40571-014-0025-4 CrossRefGoogle Scholar
  27. 27.
    He Y, Zhou Z, Cao W, Chen W (2011) Simulation of mould filling process using smoothed particle hydrodynamics. Trans Non-Ferrous Met Soc China 21:2684–2692.  https://doi.org/10.1016/S1003-6326(11)61111-4 CrossRefGoogle Scholar
  28. 28.
    Lluch E., Doste R., Giffard-Roisin S., This A., Sermesant M., Camara O., De Craene M., Morales H. Smoothed particle hydrodynamics for electrophysiological modeling: an alternative to finite element methods. In: Proceedings of the 9th international conference on functional imaging and modelling of the heart—FIMH 2017, Toronto, Canada, vol 141, pp 333–343. Springer, BerlinGoogle Scholar
  29. 29.
    Toma M (2018) The emerging use of SPH in biomedical applications. Signif Bioeng Biosci 1(1). https://pdfs.semanticscholar.org/bb44/ee090961aff9f80787ffdab66ae2558e6552.pdf. Accessed 20 July 2018
  30. 30.
    Shahriari S, Kadem L, Rogers BD, Hassan I (2012) Smoothed particle hydrodynamics method applied to pulsatile flow inside a rigid two-dimensional model of left heart cavity. Int J Numer Methods Biomed Eng 28(11):1121–1143.  https://doi.org/10.1002/cnm.2482 MathSciNetCrossRefGoogle Scholar
  31. 31.
    Al-Saad M, Kulasegaram S, Bordas S (2018) Blood flow simulation using smoothed particle hydrodynamics. In: Proceedings of the VII European congress on computational methods in applied sciences and engineering—ECCOMAS Congress 2016, Vol 4, pp 8241–8246, Crete Island, Greece, 2016. https://www.eccomas2016.org. Accessed 20 July 2018
  32. 32.
    Hieber SE, Walther JH, Koumoutsakos P (2004) Remeshed smoothed particle hydrodynamics simulation of the mechanical behavior of human organs. Technol Health Care 12(4):305–314. https://content.iospress.com/articles/technology-and-health-care/thc00339. Accessed 19 April 2019
  33. 33.
    Gómez-Gesteira M, Rogers BD, Dalrymple RA, Crespo AJC (2010) State-of-the-art of classical SPH for free-surface flows. J Hydraul Res 48:6–27.  https://doi.org/10.1080/00221686.2010.9641242 CrossRefGoogle Scholar
  34. 34.
    Xu X, Ouyang J, Yang B, Liu Z (2013) SPH simulations of three-dimensional non-Newtonian free surface flows. Comput Methods Appl Mech Eng 256:101–116.  https://doi.org/10.1016/j.cma.2012.12.017 MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Ataie-Ashtiani B, Farhadi L (2006) A stable moving-particle semi-implicit method for free surface flows. Fluid Dyn Res 38(4):241–256.  https://doi.org/10.1016/j.fluiddyn.2005.12.002 MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Gómez-Gesteira M, Dalrymple RA (2003) Using a three-dimensional smoothed particle hydrodynamics method for wave impact on a tall structure. J Waterw Port Coast Ocean Eng 130(2):63–69.  https://doi.org/10.1061/(ASCE)0733-950X(2004)130:2(63) CrossRefGoogle Scholar
  37. 37.
    Didier E, Neves DRCB, Martins R, Neves MG (2014) Wave interaction with a vertical wall: SPH numerical and experimental modelling. Ocean Eng 88:330–341.  https://doi.org/10.1016/j.oceaneng.2014.06.029 CrossRefGoogle Scholar
  38. 38.
    Vacondio R, Rogers BD, Stansby PK, Mignosa P (2013) Shallow water SPH for flooding with dynamic particle coalescing and splitting. Adv Water Resour 58:10–23.  https://doi.org/10.1016/j.advwatres.2013.04.007 CrossRefzbMATHGoogle Scholar
  39. 39.
    Liang Q, Xia X, Hou J (2015) Efficient urban flood simulation using a GPU-accelerated SPH model. Environ Earth Sci 74(11):7285–7294.  https://doi.org/10.1007/s12665-015-4753-4 CrossRefGoogle Scholar
  40. 40.
    Murotani K, Koshizuka S, Tasuku T, Shibata K, Mitsume N, Yoshimura S, Tanaka S, Hasegawa K, Nagai E, Fujisawa T (2014) Development of hierarchical domain decomposition explicit MPS method and application to large-scale tsunami analysis with floating objects. J Adv Simul Sci Eng 1(1):16–35.  https://doi.org/10.15748/jasse.1.16 CrossRefGoogle Scholar
  41. 41.
    Tilke PG, Holmes DW, Williams JR (2010) Characterizing flow in oil reservoir rock using smooth particle hydrodynamics. In: AIP conference proceedings, vol 1254, p 278.  https://doi.org/10.1063/1.3453824
  42. 42.
    Tartakovsky AM, Trask N, Pan K, Jones B, Pan W, Williams JR (2016) Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media. Comput Geosci 20(4):807–834.  https://doi.org/10.1007/s10596-015-9468-9 MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Schnabel D, Özkaya E, Biermann D, Eberhard P (2018) Modeling the motion of the cooling lubricant in drilling processes using the finite volume and the smoothed particle hydrodynamics methods. Comput Methods Appl Mech Eng 329:369–395.  https://doi.org/10.1016/j.cma.2017.09.015 MathSciNetCrossRefGoogle Scholar
  44. 44.
    Liu H, Arfaoui G, Stanic M, Montigny L, Jurkschat T, Lohner T, Stahl K (2018) Numerical modelling of oil distribution and churning gear power losses of gearboxes by smoothed particle hydrodynamics. In: Proceedings of the institution of mechanical engineers, part J: journal of engineering tribology.  https://doi.org/10.1177/1350650118760626
  45. 45.
    Dong XW, Liu GR, Li Z, Zeng W (2016) A smoothed particle hydrodynamics (SPH) model for simulating surface erosion by impacts of foreign particles. Tribol Int 95:267–278.  https://doi.org/10.1016/j.triboint.2015.11.038 CrossRefGoogle Scholar
  46. 46.
    Abdelrazek AM, Kimura I, Shimizu Y (2014) Comparison between SPH and MPS methods for numerical simulations of free surface flow problems. J Jpn Soc Civ Eng Ser. B1 (Hydraul Eng) 70(4):I_67–I_72.  https://doi.org/10.2208/jscejhe.70.i_67 Google Scholar
  47. 47.
    Fraga Filho CAD, Chacaltana JTA (2015) Study of fluid flows using Smoothed Particle Hydrodynamics: the modified pressure concept applied to quiescent fluid and dam breaking. In: Proceedings of the XXXVI Iberian Latin American congress on computational methods in engineering—CILAMCE 2015, Rio de Janeiro, Brazil.  https://doi.org/10.20906/cps/cilamce2015-0071
  48. 48.
    Fraga Filho C, Chacaltana JTA, Pinto WJN (2018) Meshless Lagrangian SPH method applied to isothermal lid-driven cavity flow at low-Re numbers. Comput Part Mech.  https://doi.org/10.1007/s40571-018-0183-x Google Scholar
  49. 49.
    Fu L, Ji Z, Hu XY, Adams NA (2019) Parallel fast-neighbor-searching and communication strategy for particle-based methods. Eng Comput.  https://doi.org/10.1108/ec-05-2018-0226 Google Scholar
  50. 50.
    Fu L, Litvinov S, Hu XY, Adams NA (2017) A novel partitioning method for block-structured adaptive meshes. J Comput Phys 341:447–473.  https://doi.org/10.1016/j.jcp.2016.11.016 MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© CIMNE, Barcelona, Spain 2019

Authors and Affiliations

  1. 1.Federal Institute of Education, Science and Technology of Espírito SantoVitóriaBrazil

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