Skip to main content
SpringerLink
Log in
Book cover

MARINE 2011, IV International Conference on Computational Methods in Marine Engineering pp 65–81Cite as

The Particle Finite Element Method (PFEM). An Effective Numerical Technique for Solving Marine, Naval and Harbour Engineering Problems

  • Chapter

  • 2675 Accesses

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 29))

Abstract

We present some developments in the Particle Finite Element Method (PFEM) for the solution of complex coupled problems in marine, naval and harbour engineering involving fluid-soil-structure interaction (FSSI). The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in a continuum domain containing fluid, soil/rock and structures subdomains. A mesh connects the nodes defining the discretized domain where the governing equations for each of the constituent materials are solved with the FEM. The stabilization for dealing with an incompressibility material is introduced via the finite calculus (FIC) method. An incremental iterative scheme for solving the non linear transient FSSI problem is described. The procedure to model frictional contact conditions and material erosion at fluid-solid and solid-solid interfaces is described. We present examples of application of the PFEM to solve FSSI problems in marine, naval and harbour engineering such as the motion of rocks by water streams, the stability of breakwaters and constructions under sea waves, the sinking of ships and the collision of a ship with ice blocks.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Idelsohn SR, Oñate E, Del Pin F, Calvo N (2002) Lagrangian formulation: the only way to solve some free-surface fluid mechanics problems. In: Mang HA, Rammerstorfer FG, Eberhardsteiner J (eds) 5th World congress on comput mechanics, Vienna, Austria, July 7–12

    Google Scholar 

  2. Idelsohn SR, Oñate E, Del Pin F (2003) A Lagrangian meshless finite element method applied to fluid-structure interaction problems. Comput Struct 81:655–671

    Article  Google Scholar 

  3. Idelsohn SR, Oñate E, Calvo N, Del Pin F (2003) The meshless finite element method. Int J Numer Methods Eng 58(6):893–912

    Article  MATH  Google Scholar 

  4. Idelsohn SR, Calvo N, Oñate E (2003) Polyhedrization of an arbitrary point set. Comput Methods Appl Mech Eng 192(22–24):2649–2668

    Article  MATH  Google Scholar 

  5. Idelsohn SR, Oñate E, Del Pin F (2004) The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves. Int J Numer Methods Eng 61:964–989

    Article  MATH  Google Scholar 

  6. Oñate E, Idelsohn SR, Del Pin F, Aubry R (2004) The particle finite element method. An overview. Int J Comput Methods 1(2):267–307

    Article  MATH  Google Scholar 

  7. Aubry R, Idelsohn SR, Oñate E (2005) Particle finite element method in fluid mechanics including thermal convection-diffusion. Comput Struct 83(17–18):1459–1475

    Article  Google Scholar 

  8. Idelsohn SR, Oñate E, Del Pin F, Calvo N (2006) Fluid-structure interaction using the particle finite element method. Comput Methods Appl Mech Eng 195:2100–2113

    Article  MATH  Google Scholar 

  9. Oñate E, García J, Idelsohn SR, Del Pin F (2006) FIC formulations for finite element analysis of incompressible flows. Eulerian, ALE and Lagrangian approaches. Comput Methods Appl Mech Eng 195(23–24):3001–3037

    Article  MATH  Google Scholar 

  10. Oñate E, Celigueta MA, Idelsohn SR (2006) Modeling bed erosion in free surface flows by the particle finite element method. Acta Geotech 1(4):237–252

    Article  Google Scholar 

  11. Del Pin F, Idelsohn SR, Oñate E, Aubry R (2007) The ALE/Lagrangian particle finite element method: a new approach to computation of free-surface flows and fluid-object interactions. Comput Fluids 36:27–38

    Article  MATH  Google Scholar 

  12. Idelsohn SR, Marti J, Limache A, Oñate E (2008) Unified Lagrangian formulation for elastic solids and incompressible fluids: application to fluid-structure interaction problems via the PFEM. Comput Methods Appl Mech Eng 197:1762–1776

    Article  MATH  Google Scholar 

  13. Larese A, Rossi R, Oñate E, Idelsohn SR (2008) Validation of the particle finite element method (PFEM) for free surface flows. Eng Comput 25(4):385–425

    Article  MATH  Google Scholar 

  14. Oñate E, Idelsohn SR, Celigueta MA, Rossi R (2008) Advances in the particle finite element method for the analysis of fluid-multibody interaction and bed erosion in free surface flows. Comput Methods Appl Mech Eng 197(19–20):1777–1800

    Article  MATH  Google Scholar 

  15. Idelsohn SR, Mier-Torrecilla M, Oñate E (2009) Multi-fluid flows with the particle finite element method. Comput Methods Appl Mech Eng 198:2750–2767

    Article  MATH  Google Scholar 

  16. Carbonell JM, Oñate E, Suárez B (2010) Modeling of ground excavation with the particle finite element method. J Eng Mech 136(4):455–463

    Article  Google Scholar 

  17. Oñate E, Rossi R, Idelsohn SR, Butler K (2010) Melting and spread of polymers in fire with the particle finite element method. Int J Numer Methods Eng 81(8):1046–1072

    MATH  Google Scholar 

  18. Oñate E, Celigueta MA, Idelsohn SR, Salazar F, Suárez B (2011) Possibilities of the particle finite element method for fluid–soil–structure interaction problems. Comput Mech 48:307–318

    Article  MathSciNet  MATH  Google Scholar 

  19. Edelsbrunner H, Mucke EP (1999) Three dimensional alpha shapes. ACM Trans Graph 13:43–72

    Article  Google Scholar 

  20. Oñate E (1998) Derivation of stabilized equations for advective-diffusive transport and fluid flow problems. Comput Methods Appl Mech Eng 151:233–267

    Article  MATH  Google Scholar 

  21. Oñate E (2004) Possibilities of finite calculus in computational mechanics. Int J Numer Methods Eng 60(1):255–281

    Article  MATH  Google Scholar 

  22. Oñate E, García J (2001) A finite element method for fluid-structure interaction with surface waves using a finite calculus formulation. Comput Methods Appl Mech Eng 191:635–660

    Article  MATH  Google Scholar 

  23. Oñate E, Valls A, García J (2006) FIC/FEM formulation with matrix stabilizing terms for incompressible flows at low and high Reynold’s numbers. Comput Mech 38(4–5):440–455

    Article  MATH  Google Scholar 

  24. Zienkiewicz OC, Taylor RL (2005) The finite element method for solid and structural mechanics. Elsevier, Amsterdam

    MATH  Google Scholar 

  25. Donea J, Huerta A (2003) Finite element method for flow problems. Wiley, New York

    Book  Google Scholar 

  26. Zienkiewicz OC, Taylor RL, Zhu JZ (2005) The finite element method. Its basis and fundamentals. Elsevier, Amsterdam

    Google Scholar 

  27. Zienkiewicz OC, Taylor RL, Nithiarasu P (2006) The finite element method for fluid dynamics. Elsevier, Amsterdam

    Google Scholar 

  28. Archard JF (1953) Contact and rubbing of flat surfaces. J Appl Phys 24(8):981–988

    Article  Google Scholar 

Download references

Acknowledgements

This research was partially supported by projects SAFECON and REALTIME of the European Research Council of the European Commission (EC).

Author information

Authors and Affiliations

  1. International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain

    E. Oñate & M. A. Celigueta

  2. ICREA Research Professor at CIMNE, Barcelona, Spain

    S. R. Idelsohn

  3. Universitat Politècnica de Catalunya (UPC), Barcelona, Spain

    B. Suárez

Authors
  1. E. Oñate
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. R. Idelsohn
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. A. Celigueta
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. B. Suárez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Oñate .

Editor information

Editors and Affiliations

  1. Mechanical Engineering, Instituto Superior Técnico, Avenida Rovisco Pais 1, Lisbon, 1049 001, Portugal

    Luís Eça

  2. CIMNE, Technical University of Catalonia (UPC), Gran Capitan, s/n, Barcelona, 08034, Spain

    Eugenio Oñate

  3. Universitat Politècnica de Catalunya, EDIFICI NT1 FNB-CIMNE PLAÇA PALAU 18, S/N, Barcelona, 08003, Spain

    Julio García-Espinosa

  4. Norwegian Univ. of Science & Technology, Alfred Getz vei 1, Trondheim, 7491, Norway

    Trond Kvamsdal

  5. Norwegian Univ. of Science & Technology, Alfred Getz vei 1, Trondheim, 7491, Norway

    Pål Bergan

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Oñate, E., Idelsohn, S.R., Celigueta, M.A., Suárez, B. (2013). The Particle Finite Element Method (PFEM). An Effective Numerical Technique for Solving Marine, Naval and Harbour Engineering Problems. In: Eça, L., Oñate, E., García-Espinosa, J., Kvamsdal, T., Bergan, P. (eds) MARINE 2011, IV International Conference on Computational Methods in Marine Engineering. Computational Methods in Applied Sciences, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6143-8_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-6143-8_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-6142-1

  • Online ISBN: 978-94-007-6143-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation