Skip to main content
SpringerLink
Log in

Free surface tension in incompressible smoothed particle hydrodynamcis (ISPH)

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

A Letter to this article was published on 28 December 2021

Abstract

In this work a Dirichlet pressure boundary condition for incompressible Smoothed Particle Hydrodynamics (SPH) is presented for free surfaces under surface tension. These free surfaces occur when the surrounding phase in simulations is neglected for computational reasons while the effects of the surface tension shall remain. We demonstrate capabilities of the boundary condition by comparing it to an approach from the literature. The simulations show that our approach provides a higher stability to the free surface, being capable of capturing static and transient processes as much as bubble coalescence. Furthermore a new approach is presented to compute the curvature more exactly for three-dimensional cases in order to stabilize the simulation, which is applicable for weakly compressible SPH and incompressible SPH simulations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Adami S, Hu X, Adams N (2010) A new surface-tension formulation for multi-phase SPH using a reproducing divergence approximation. J Comput Phys 229(13):5011–5021

    Article  Google Scholar 

  2. Aly AM, Asai M, Sonda Y (2013) Modelling of surface tension force for free surface flows in ISPH method. Int J Numer Methods Heat Fluid Flow 23(3):479–498

    Article  MathSciNet  Google Scholar 

  3. Blank M, Nair P, Pöschel T (2019) Capillary viscous flow and melting dynamics: coupled simulations for additive manufacturing applications. Int J Heat Mass Transf 131:1232–1246

    Article  Google Scholar 

  4. Bøckmann A, Shipilova O, Skeie G (2012) Incompressible SPH for free surface flows. Comput Fluids 67:138–151

    Article  MathSciNet  Google Scholar 

  5. Brackbill J, Kothe DB, Zemach C (1992) A continuum method for modeling surface tension. J Comput Phys 100(2):335–354

    Article  MathSciNet  Google Scholar 

  6. Cleary PW (1998) Modelling confined multi-material heat and mass flows using SPH. Appl Math Modell 22(12):981–993

    Article  Google Scholar 

  7. Cleary PW, Monaghan JJ (1999) Conduction modelling using smoothed particle hydrodynamics. J Comput Phys 148(1):227–264

    Article  MathSciNet  Google Scholar 

  8. Colagrossi A, Antuono M, Souto-Iglesias A, Le Touzé D (2011) Theoretical analysis and numerical verification of the consistency of viscous smoothed-particle-hydrodynamics formulations in simulating free-surface flows. Phys Rev E 84:026705. https://doi.org/10.1103/PhysRevE.84.026705

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. Crespo AJ, Domínguez JM, Rogers BD, Gómez-Gesteira M, Longshaw S, Canelas R, Vacondio R, Barreiro A, García-Feal O (2015) Dualsphysics: open-source parallel cfd solver based on smoothed particle hydrodynamics (SPH). Comput Phys Commun 187:204–216

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  12. Fürstenau JP, Avci B, Wriggers P (2016) A numerical review of multi-fluid SPH algorithms for high density ratios. In: Bazilevs Y, Takizawa K (eds) Advances in computational fluid-structure interaction and flow simulation. Modeling and simulation in science, engineering and technology. Birkhäuser, Cham, pp 139–150

  13. Fürstenau JP, Avci B, Wriggers P (2017) A comparative numerical study of pressure-poisson-equation discretization strategies for SPH. In: 12th international SPHERIC workshop, Ourense, Spain, pp 1–8

  14. Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 181(3):375–389

    Article  Google Scholar 

  15. Grenier N, Antuono M, Colagrossi A, Le Touzé D, Alessandrini B (2009) An hamiltonian interface SPH formulation for multi-fluid and free surface flows. J Comput Phys 228(22):8380–8393

    Article  MathSciNet  Google Scholar 

  16. Hirschler M, Kunz P, Huber M, Hahn F, Nieken U (2016) Open boundary conditions for ISPH and their application to micro-flow. J Comput Phys 307:614–633

    Article  MathSciNet  Google Scholar 

  17. Hirschler M, Oger G, Nieken U, Le Touzé D (2017) Modeling of droplet collisions using smoothed particle hydrodynamics. Int J Multiph Flow 95:175–187

    Article  MathSciNet  Google Scholar 

  18. Hu H, Eberhard P (2017) Thermomechanically coupled conduction mode laser welding simulations using smoothed particle hydrodynamics. Comput Part Mech 4(4):473–486. https://doi.org/10.1007/s40571-016-0140-5

    Article  Google Scholar 

  19. Hu XY, Adams NA (2006) A multi-phase SPH method for macroscopic and mesoscopic flows. J Comput Phys 213(2):844–861

    Article  MathSciNet  Google Scholar 

  20. Ihmsen M, Cornelis J, Solenthaler B, Horvath C, Teschner M (2014) Implicit incompressible SPH. IEEE Trans Vis Comput Gr 20(3):426–435

    Article  Google Scholar 

  21. Landau L, Lifshitz E (1959) Course of theoretical physics. Fluid mechanics, vol 6. Elsevier, London

    Google Scholar 

  22. Lind S, Xu R, Stansby P, Rogers B (2012) Incompressible smoothed particle hydrodynamics for free-surface flows: a generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves. J Comput Phys 231(4):1499–1523

    Article  MathSciNet  Google Scholar 

  23. Liu GR, Liu MB (2003) Smoothed particle hydrodynamics: a meshfree particle method. World Scientific, Singapore

    Book  Google Scholar 

  24. Lukarski D, Trost N (2014) Paralution project. http://www.paralution.com

  25. Monaghan J, Rafiee A (2013) A simple SPH algorithm for multi-fluid flow with high density ratios. Int J Numer Methods Fluids 71(5):537–561

    Article  MathSciNet  Google Scholar 

  26. Monaghan JJ (1982) Why particle methods work. SIAM J Sci Stat Comput 3(4):422–433

    Article  MathSciNet  Google Scholar 

  27. Monaghan JJ (1992) Smoothed particle hydrodynamics. Annu Rev Astron Astrophys 30(1):543–574

    Article  Google Scholar 

  28. Morris JP (2000) Simulating surface tension with smoothed particle hydrodynamics. Int J Numer Methods Fluids 33(3):333–353

    Article  Google Scholar 

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

    Article  Google Scholar 

  30. Nair P, Tomar G (2014) An improved free surface modeling for incompressible SPH. Comput Fluids 102:304–314

    Article  MathSciNet  Google Scholar 

  31. Nair P, Tomar G (2019) Simulations of gas-liquid compressible-incompressible systems using SPH. Comput Fluids 179:301–308

    Article  MathSciNet  Google Scholar 

  32. Oger G, Doring M, Alessandrini B, Ferrant P (2007) An improved SPH method: towards higher order convergence. J Comput Phys 225(2):1472–1492

    Article  MathSciNet  Google Scholar 

  33. Rider WJ (1995) Approximate projection methods for incompressible flow: implementation, variants and robustness. In: LANL UNCLASSIFIED REPORT LA-UR-94-2000, LOS ALAMOS NATIONAL LABORATORY. Citeseer

  34. Russell M, Souto-Iglesias A, Zohdi T (2018) Numerical simulation of laser fusion additive manufacturing processes using the SPH method. Comput Methods Appl Mech Eng 341:163–187

    Article  MathSciNet  Google Scholar 

  35. Shao S, Lo EY (2003) Incompressible SPH method for simulating newtonian and non-newtonian flows with a free surface. Adv Water Resour 26(7):787–800

    Article  Google Scholar 

  36. Shepard D (1968) A two-dimensional interpolation function for irregularly-spaced data. In: Proceedings of the 1968 23rd ACM national conference. ACM, pp 517–524

  37. Szewc K, Tanière A, Pozorski J, Minier JP (2012) A study on application of smoothed particle hydrodynamics to multi-phase flows. Int J Nonlinear Sci Numer Simul 13(6):383–395

    Article  MathSciNet  Google Scholar 

  38. Wendland H (1995) Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv Comput Math 4(1):389–396. https://doi.org/10.1007/BF02123482

    Article  MathSciNet  MATH  Google Scholar 

  39. Zhang M (2010) Simulation of surface tension in 2d and 3d with smoothed particle hydrodynamics method. J Comput Phys 229(19):7238–7259

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Continuum Mechanics, Leibniz University Hannover, Appelstraße 11, 30167, Hannover, Germany

    Jan-Philipp Fürstenau, Christian Weißenfels & Peter Wriggers

Authors
  1. Jan-Philipp Fürstenau
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christian Weißenfels
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peter Wriggers
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jan-Philipp Fürstenau.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

1.1 Square bubble

See Fig. 17.

Fig. 17
figure 17

Plots of the square bubble test case after 0.01, 0.03, 0.05, 0.07, 0.09   s, simulated with our own approach with the lowest and highest resolution [right] and simulated with the approach according to Hirschler with the lowest and the highest resolution [right]

Full size image

1.2 3D bubble collision

See Fig. 18.

Fig. 18
figure 18

Plots of the three dimensional bubble shapes for the centric bubble collision at \(\tau = 0, 0.3125, 0.725, 1.3125\) and 2 [left] and for the eccentric bubble collision at \(\tau = 0, 0.375, 0.5625, 0.875\) and 2.8125 [right]

Full size image

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fürstenau, JP., Weißenfels, C. & Wriggers, P. Free surface tension in incompressible smoothed particle hydrodynamcis (ISPH). Comput Mech 65, 487–502 (2020). https://doi.org/10.1007/s00466-019-01780-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-019-01780-6

Keywords

Search

Navigation