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Smoothed Particle Hydrodynamics

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Simulation of Additive Manufacturing using Meshfree Methods

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 97))

Abstract

Smoothed Particle Hydrodynamics (SPH) has experienced a renaissance in computational mechanics in recent years. Due to the increased computing power, the additional effort due to the search algorithm, among other things, is no longer so significant. Nevertheless, some shortcomings are still present as will be shown in this chapter.

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References

  • S. Adami, X.Y. Hu, N.A. Adams, A generalized wall boundary condition for smoothed particle hydrodynamics. J. Comput. Phys. 231(21), 7057–7075 (2012)

    Article  MathSciNet  Google Scholar 

  • S. Adami, X.Y. Hu, N.A. Adams, A transport-velocity formulation for smoothed particle hydrodynamics. J. Comput. Phys. 241, 292–307 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • C. Antoci, M. Gallati, S. Sibilla, Numerical simulation of fluid-structure interaction by SPH. Comput. Struct. 85(11–14), 879–890 (2007)

    Article  Google Scholar 

  • M. Antuono, A. Colagrossi, S. Marrone, Numerical diffusive terms in weakly-compressible SPH schemes. Comput. Phys. Commun. 183(12), 2570–2580 (2012)

    Article  MathSciNet  Google Scholar 

  • T. Belytschko, Y. Krongauz, J. Dolbow, C. Gerlach, On the completeness of meshfree particle methods. Int. J. Numer. Methods Eng. 43(5), 785–819 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  • T. Belytschko, Y. Guo, W.K. Liu, S.P. Xiao, A unified stability analysis of meshless particle methods. Int. J. Numer. Methods Eng. 48(9), 1359–1400 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  • J. Bonet, S.D. Kulasegaram, Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations. Int. J. Numer. Methods Eng. 47(6), 1189–1214 (2000)

    Article  MATH  Google Scholar 

  • J. Bonet, T.S.L. Lok, Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Comput. Methods Appl. Mech. Eng. 180(1–2), 97–115 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • L. Brookshaw, A method of calculating radiative heat diffusion in particle simulations. Publ. Astron. Soc. Aust. 6(2), 207–210 (1985)

    Article  Google Scholar 

  • A. Colagrossi, M. Landrini, Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J. Comput. Phys. 191(2), 448–475 (2003)

    Article  MATH  Google Scholar 

  • S.J. Cummins, M. Rudman, An SPH projection method. J. Comput. Phys. 152(2), 584–607 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • C.T. Dyka, R.P. Ingel, An approach for tension instability in Smoothed Particle Hydrodynamics (SPH). Comput. Struct. 57(4), 573–580 (1995)

    Article  MATH  Google Scholar 

  • C.T. Dyka, P.W. Randles, R.P. Ingel, Stress points for tension instability in SPH. Int. J. Numer. Methods Eng. 40(13), 2325–2341 (1997)

    Article  MATH  Google Scholar 

  • P. Espanol, M. Revenga, Smoothed dissipative particle dynamics. Phys. Rev. E 67(2), 026705 (2003)

    Article  Google Scholar 

  • M. Ferrand, D.R. Laurence, B.D. Rogers, D. Violeau, C. Kassiotis, Unified semi-analytical wall boundary conditions for inviscid, laminar or turbulent flows in the meshless SPH method. Int. J. Numer. Methods Fluids 71(4), 446–472 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  • J.P. Fürstenau, H. Wessels, C. Weißenfels, P. Wriggers, Generating virtual process maps of SLM using powder scale SPH simulations. Comput. Part. Mech. 339, 91–114 (2019)

    Google Scholar 

  • G.C. Ganzenmüller, An hourglass control algorithm for Lagrangian Smooth Particle Hydrodynamics. Comput. Methods Appl. Mech. Eng. 286, 87–106 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • R.A. Gingold, J.J. Monaghan, Smoothed Particle Hydrodynamics: theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181, 375–389 (1977)

    Article  MATH  Google Scholar 

  • R.A. Gingold, J.J. Monaghan, Kernel estimates as a basis for general particle methods in hydrodynamics. J. Comput. Phys. 46(3), 429–453 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  • X.Y. Hu, N.A. Adams, An incompressible multi-phase SPH method. J. Comput. Phys. 227(1), 264–278 (2007)

    Article  MATH  Google Scholar 

  • S. Kulasegaram, J. Bonet, R.W. Lewis, M. Profit, A variational formulation based contact algorithm for rigid boundaries in two-dimensional SPH applications. Comput. Mech. 33(4), 316–325 (2004)

    Article  MATH  Google Scholar 

  • S. Li, W.K. Liu, Meshfree Particle Methods (Springer, Berlin, Heidelberg, New York, 2007)

    Google Scholar 

  • L.D. Libersky, A.G. Petschek, T.C. Carney, J.R. Hipp, F.A. Allahdadi, High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response. J. Comput. Phys. 109(1), 67–75 (1993)

    Article  MATH  Google Scholar 

  • G.R. Liu, M.B. Liu, Smoothed Particle Hydrodynamics: A Meshfree Particle Method (World Scientific, 2003)

    Google Scholar 

  • L.B. Lucy, Numerical approach to testing the fission hypothesis. Astron. J. 82, 1013–1024 (1977)

    Article  Google Scholar 

  • J.R. MacDonald, Some simple isothermal equations of state. Rev. Mod. Phys. 38(4), 669–679 (1966)

    Article  Google Scholar 

  • F. Macia, M. Antuono, L.M. González, A. Colagrossi, Theoretical analysis of the no-slip boundary condition enforcement in SPH methods. Prog. Theor. Phys. 125(6), 1091–1121 (2011)

    Article  MATH  Google Scholar 

  • F. Macia, L.M. González, J.L. Cercos-Pita, A. Souto-Iglesias, A boundary integral SPH formulation: consistency and applications to ISPH and WCSPH. Prog. Theor. Phys. 128(3), 439–462 (2012)

    Article  MATH  Google Scholar 

  • J.C. Marongiu, F. Leboeuf, J. Caro, E. Parkinson, Free surface flows simulations in Pelton turbines using an hybrid SPH-ALE method. J. Hydraul. Res. 48(S1), 40–49 (2010)

    Article  Google Scholar 

  • S. Marrone, M.A.G.D. Antuono, A. Colagrossi, G. Colicchio, D. Le Touzé, G. Graziani, \(\delta \)-SPH model for simulating violent impact flows. Comput. Methods Appl. Mech. Eng. 200(13–16), 1526–1542 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • D. Molteni, A. Colagrossi, A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH. Comput. Phys. Commun. 180(6), 861–872 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • J.J. Monaghan, An introduction to SPH. Comput. Phys. Commun. 48(1), 89–96 (1988)

    Article  MATH  Google Scholar 

  • J.J. Monaghan, On the problem of penetration in particle methods. J. Comput. Phys. 82(1), 1–15 (1989)

    Article  MATH  Google Scholar 

  • J.J. Monaghan, Smoothed Particle Hydrodynamics. Ann. Rev. Astron. Astrophys. 30(1), 543–574 (1992)

    Article  Google Scholar 

  • J.J. Monaghan, Simulating free surface flows with SPH. J. Comput. Phys. 110(2), 399–406 (1994)

    Article  MATH  Google Scholar 

  • J.J. Monaghan, SPH without a tensile instability. J. Comput. Phys. 159(2), 290–311 (2000)

    Article  MATH  Google Scholar 

  • J.J. Monaghan, SPH compressible turbulence. Mon. Not. R. Astron. Soc. 335(3), 843–852 (2002)

    Article  Google Scholar 

  • J.J. Monaghan, Smoothed Particle Hydrodynamics. Rep. Prog. Phys. 68(8), 1703–1759 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • J.J. Monaghan, R.A. Gingold, Shock simulation by the particle method SPH. J. Comput. Phys. 52(2), 374–389 (1983)

    Article  MATH  Google Scholar 

  • J.J. Monaghan, J.B. Kajtar, SPH particle boundary forces for arbitrary boundaries. Comput. Phys. Commun. 180(10), 1811–1820 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • J.P. Morris, P.J. Fox, Y. Zhu, Modeling low reynolds number incompressible flows using SPH. J. Comput. Phys. 136(1), 214–226 (1997)

    Article  MATH  Google Scholar 

  • R.P. Nelson, J.C.B. Papaloizou, Variable smoothing lengths and energy conservation in Smoothed Particle Hydrodynamics. Mon. Not. R. Astron. Soc. 270(1), 1–20 (1994)

    Article  Google Scholar 

  • G. Oger, S. Marrone, D. Le Touzé, M. De Leffe, SPH accuracy improvement through the combination of a quasi-Lagrangian shifting transport velocity and consistent ALE formalisms. J. Comput. Phys. 313, 76–98 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  • D.J. Price, Smoothed particle hydrodynamics and magnetohydrodynamics. J. Comput. Phys. 231(3), 759–794 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  • D.J. Price, J.J. Monaghan, Smoothed particle magnetohydrodynamics–II. Variational principles and variable smoothing-length terms. Mon. Not. R. Astron. Soc. 348(1), 139–152 (2004)

    Google Scholar 

  • T. Rabczuk, T. Belytschko, S.P. Xiao, Stable particle methods based on Lagrangian kernels. Comput. Methods Appl. Mech. Eng. 193(12–14), 1035–1063 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • P.W. Randles, L.D. Libersky, Smoothed Particle Hydrodynamics: some recent improvements and applications. Comput. Methods Appl. Mech. Eng. 139(1–4), 375–408 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • P.W. Randles, L.D. Libersky, Normalized SPH with stress points. Int. J. Numer. Methods Eng. 48(10), 1445–1462 (2000)

    Article  MATH  Google Scholar 

  • S. Shao, E.Y.M. Lo, Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Adv. Water Resour. 26(7), 787–800 (2003)

    Article  Google Scholar 

  • M. Soleimani, Numerical Simulation and Experimental Validation of Biofilm Formation. Ph.D. thesis, Institut für Kontinuumsmechanik, Gottfried Wilhelm Leibniz Universität (2017)

    Google Scholar 

  • J.W. Swegle, D.L. Hicks, S.W. Attaway, Smoothed Particle Hydrodynamics stability analysis. J. Comput. Phys. 116(1), 123–134 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • H. Takeda, S.M. Miyama, M. Sekiya, Numerical simulation of viscous flow by Smoothed Particle Hydrodynamics. Prog. Theor. Phys. 92(5), 939–960 (1994)

    Article  Google Scholar 

  • A. Valizadeh, J.J. Monaghan, A study of solid wall models for weakly compressible SPH. J. Comput. Phys. 300, 5–19 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • R. Vignjevic, J. Campbell, L. Libersky, A treatment of zero-energy modes in the Smoothed Particle Hydrodynamics method. Comput. Methods Appl. Mech. Eng. 184(1), 67–85 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  • J.P. Vila, On particle weighted methods and Smooth Particle Hydrodynamics. Math. Models Methods Appl. Sci. 9(02), 161–209 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • H. Wendland, Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv. Comput. Math. 4(1), 389–396 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • R. Xu, P. Stansby, D. Laurence, Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach. J. Comput. Phys. 228(18), 6703–6725 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Christian Weißenfels .

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Weißenfels, C. (2022). Smoothed Particle Hydrodynamics. In: Simulation of Additive Manufacturing using Meshfree Methods. Lecture Notes in Applied and Computational Mechanics, vol 97. Springer, Cham. https://doi.org/10.1007/978-3-030-87337-0_6

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  • DOI: https://doi.org/10.1007/978-3-030-87337-0_6

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