Skip to main content
SpringerLink
Log in

Unified semi-analytical wall boundary conditions in SPH: analytical extension to 3-D

  • Original Paper
  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

Solid wall boundary conditions have been an area of active research within the context of Smoothed Particle Hydrodynamics (SPH) for quite a while. Ferrand et al. (Int. J. Numer. Methods Fluids 71(4), 446–472, 2012) presented a novel approach using a renormalization factor in the SPH approximation. The computation of this factor depends on an integral along the boundary of the domain and in their original paper Ferrand et al. gave an analytical formulation for the 2-D case using the Wendland kernel. In this paper the formulation will be extended to 3-D, again providing analytical formulae. Due to the boundary being two dimensional a domain decomposition algorithm needs to be employed in order to obtain special integration domains. For these the analytical formulae will be presented when using the Wendland kernel. The algorithm presented within this paper is applied to several academic test-cases for which either analytical results or simulations with other methods are available. It will be shown that the present formulation produces accurate results and provides a significant improvement compared to approximative methods.

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

Similar content being viewed by others

References

  1. Amicarelli, A., Agate, G., Guandalini, R.: Development and validation of a SPH model using discrete surface elements at boundaries. In: Proceedings of the 7th International SPHERIC Workshop, pp. 369–374. Prato (2012)

  2. Crespo, A.C., Dominguez, J.M., Barreiro, A., Gómez-Gesteira, M., Rogers, B.D.: GPUs, a new tool of acceleration in CFD: efficiency and reliability on smoothed particle hydrodynamics methods. PLoS ONE 6(6), e20,685 (2011). doi:10.1371/journal.pone.0020685

    Article  Google Scholar 

  3. Dalrymple, R.A., Knio, O.: SPH modelling of water waves. In: H. Hanson, M. Larson (eds.) ASCE Conference Proceedings, vol. 260, p. 80. 20Lund, Sweden (2001). doi:10.1061/40566(260)80. http://link.aip.org/link/?ASC/260/80/1

  4. Ferrand, M., Laurence, D., Rogers, B.D., Violeau, D., Kassiotis, C.: 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 (2012). doi:10.1002/fld.3666

    Article  MathSciNet  Google Scholar 

  5. Gingold, R.A., Monaghan, J.J.: Smoothed particle hydrodynamics - theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181, 375–389 (1977). http://adsabs.harvard.edu/abs/1977MNRAS.181..375G

    Article  MATH  Google Scholar 

  6. Kleefsman, K., Fekken, G., Veldman, A., Iwanowski, B., Buchner, B.: A volume-of-fluid based simulation method for wave impact problems. J. Comput. Phys. 206(1), 363–393 (2005). doi:10.1016/j.jcp.2004.12.007. http://www.sciencedirect.com/science/article/pii/S0021999104005170

    Article  MATH  MathSciNet  Google Scholar 

  7. Libersky, L.D., Petschek, A.G., Carney, T.C., Hipp, J.R., Allahdadi, F.A.: High strain lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response. J. Comput. Phys. 109(1), 67–75 (1993). doi:10.1006/jcph.1993.1199. http://www.sciencedirect.com/science/article/pii/S002199918371199X

    Article  MATH  Google Scholar 

  8. Lucy, L.B.: A numerical approach to the testing of the fission hypothesis. Astron. J. 82, 1013–1024 (1977). http://adsabs.harvard.edu/abs/1977AJ.....82.1013L

    Article  Google Scholar 

  9. Mayrhofer, A., Rogers, B.D., Violeau, D., Ferrand, M.: Investigation of wall bounded flows using SPH and the unified semi-analytical wall boundary conditions. Comput. Phys. Commun. 184(11), 2515–2527 (2013). doi:10.1016/j.cpc.2013.07.004. http://www.sciencedirect.com/science/article/pii/S0010465513002324

    Article  MathSciNet  Google Scholar 

  10. Monaghan, J.: Smoothed particle hydrodynamics. Ann. Rev. Astron. Astrophys. 30, 543–574 (1992)

    Article  Google Scholar 

  11. Monaghan, J., Kajtar, J.: SPH particle boundary forces for arbitrary boundaries. Comput. Phys. Commun. 180(10), 1811–1820 (2009). doi:10.1016/j.cpc.2009.05.008. http://www.sciencedirect.com/science/article/ pii/S0010465509001544

    Article  MATH  MathSciNet  Google Scholar 

  12. Monaghan, J.J.: Simulating free surface flows with SPH. J. Comput. Phys. 110, 399–406 (1994). http://adsabs.harvard.edu/abs/1994JCoPh.110..399M

    Article  MATH  Google Scholar 

  13. Violeau, D.: Fluid Mechanics and the SPH Method: Theory and Applications. Oxford University Press (2012). http://ukcatalogue.oup.com/product/academic/earthsciences/hydrology/9780199655526.do

  14. Weller, H., Greenshields, C., Janssens, M.: OpenFOAM (2012). www.openfoam.org

Download references

Author information

Authors and Affiliations

  1. School of MACE, University of Manchester, Manchester, UK

    Arno Mayrhofer

  2. EDF R&D, Paris, France

    Martin Ferrand & Damien Violeau

  3. Ecole des Ponts ParisTech, Champs-sur-Marne, France

    Christophe Kassiotis

  4. Saint-Venant Laboratory for Hydraulics, Université Paris-Est, Paris, France

    Christophe Kassiotis & Damien Violeau

  5. Sequans Communications, Paris, France

    François-Xavier Morel

Authors
  1. Arno Mayrhofer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martin Ferrand
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christophe Kassiotis
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Damien Violeau
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. François-Xavier Morel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arno Mayrhofer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mayrhofer, A., Ferrand, M., Kassiotis, C. et al. Unified semi-analytical wall boundary conditions in SPH: analytical extension to 3-D. Numer Algor 68, 15–34 (2015). https://doi.org/10.1007/s11075-014-9835-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11075-014-9835-y

Keywords

Search

Navigation