Advertisement

Computational Particle Mechanics

, Volume 4, Issue 3, pp 331–343 | Cite as

On the effect of standard PFEM remeshing on volume conservation in free-surface fluid flow problems

  • Alessandro Franci
  • Massimiliano Cremonesi
Article

Abstract

The aim of this work is to analyze the remeshing procedure used in the particle finite element method (PFEM) and to investigate how this operation may affect the numerical results. The PFEM remeshing algorithm combines the Delaunay triangulation and the Alpha Shape method to guarantee a good quality of the Lagrangian mesh also in large deformation processes. However, this strategy may lead to local variations of the topology that may cause an artificial change of the global volume. The issue of volume conservation is here studied in detail. An accurate description of all the situations that may induce a volume variation during the PFEM regeneration of the mesh is provided. Moreover, the crucial role of the parameter \(\alpha \) used in the Alpha Shape method is highlighted and a range of values of \(\alpha \) for which the differences between the numerical results are negligible, is found. Furthermore, it is shown that the variation of volume induced by the remeshing reduces by refining the mesh. This check of convergence is of paramount importance for the reliability of the PFEM. The study is carried out for 2D free-surface fluid dynamics problems, however the conclusions can be extended to 3D and to all those problems characterized by significant variations of internal and external boundaries.

Keywords

Particle finite element method Volume conservation Alpha shape Remeshing 

References

  1. 1.
    Aubry R, Idelsohn SR, Oñate E (2005) Particle finite element method in fluid-mechanics including thermal convection-diffusion. Comput Struct 83:1459–1475CrossRefGoogle Scholar
  2. 2.
    Aubry R, Oñate E, Idelsohn SR (2006) Fractional step like schemes for free surface problems with thermal coupling using the lagrangian PFEM. comput mech 38(4–5):294–309MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Brezzi F (1974) On the existence, uniqueness and approximation of saddle-point problems arising from lagrange multipliers. Revue française d’automatique, informatique, recherche opérationnelle. Série rouge. Analyse numérique 8(R–2):129–151CrossRefzbMATHGoogle Scholar
  4. 4.
    Cante J, Davalos C, Hernandez JA, Oliver J, Jonsen P, Gustafsson G, Haggblad H (2014) Pfem-based modeling of industrial granular flows. Comput Part Mech 1(1):47–70CrossRefGoogle Scholar
  5. 5.
    Carbonell JM (2009) Doctoral thesis: modeling of ground excavation with the particle finite element method. Universitat Politècnica de CatalunyaGoogle Scholar
  6. 6.
    Carbonell JM, Oñate E, Suarez B (2010) Modeling of ground excavation with the particle finite-element method. J Eng Mech 136:455–463CrossRefGoogle Scholar
  7. 7.
    Carbonell JM, Oñate E, Suarez B (2013) Modelling of tunnelling processes and cutting tool wear with the particle finite element method (pfem). Comput Mech 52(3):607–629CrossRefzbMATHGoogle Scholar
  8. 8.
    Cremonesi M, Ferrara L, Frangi A, Perego U (2010) Simulation of the flow of fresh cement suspensions by a lagrangian finite element approach. J Non-Newton Fluid Mech 165:1555–1563CrossRefzbMATHGoogle Scholar
  9. 9.
    Cremonesi M, Frangi A, Perego U (2010) A lagrangian finite element approach for the analysis of fluid-structure interaction problems. Int J Numer Methods Eng 84:610–630MathSciNetzbMATHGoogle Scholar
  10. 10.
    Cremonesi M, Frangi A, Perego U (2011) A lagrangian finite element approach for the simulation of water-waves induced by landslides. Comput Struct 89:1086–1093CrossRefGoogle Scholar
  11. 11.
    Edelsbrunner H, Mucke EP (1999) Three dimensional alpha shapes. ACM Trans Graph 13:43–72CrossRefzbMATHGoogle Scholar
  12. 12.
    Edelsbrunner H, Tan TS (1993) An upper bound for conforming delaunay triangulations. Discrete Comput Geom 10(2):197:213MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Franci A (2016) Unified Lagrangian formulation for fluid and solid mechanics, fluid-structure interaction and coupled thermal problems using the PFEM. Springer Theses, Springer International Publishing, SwitzerlandGoogle Scholar
  14. 14.
    Franci A, Oñate E, Carbonell JM (2015) On the effect of the bulk tangent matrix in partitioned solution schemes for nearly incompressible fluids. Int J Numer Methods Eng 102:257–277MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Franci A, Oñate E, Carbonell JM (2016) Unified lagrangian formulation for solid and fluid mechanics and fsi problems. Comput Methods Appl Mech Eng 298:520–547MathSciNetCrossRefGoogle Scholar
  16. 16.
    Greaves DM (2006) Simulation of viscous water column collapse using adapting hierarchical grids. Int J Numer Methods Eng 50:693–711CrossRefzbMATHGoogle Scholar
  17. 17.
    Idelsohn SR, Storti MA, Oñate E (2001) Lagrangian formulations to solve free surface incompressible inviscid fluid flows. Comput Methods Appl Mech Eng 191(6–7):583–593MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Idelsohn SR, Calvo N, Oñate E (2003) Polyhedrization of an arbitrary point set. Comput Methods Appl Mech Eng 92(22–24):2649–2668CrossRefzbMATHGoogle Scholar
  19. 19.
    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 61:964–989MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Idelsohn SR, Oñate E, Del Pin F, Calvo N (2006) Fluid-structure interaction using the particle finite element method. Comput Methods Appl Mech Eng 195:2100–2113MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Idelsohn SR, Marti J, Limache A, Oñate E (2008) Unified lagrangian formulation for elastic solids and incompressible fluids: Applications to fluid-structure interaction problems via the pfem. Comput Methods Appl Mech Eng 197:1762–1776MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Idelsohn SR, Oñate E (2006) To mesh or not to mesh. That is the question. Comput Methods Appl Mech Eng 195:4681–4696MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Idelsohn SR, Oñate E (2008) The challenge of mass conservation in the solution of free surface flows with the fractional step method. problems and solutions. Commun Numer Methods Eng 26(10):1313–1330MathSciNetzbMATHGoogle Scholar
  24. 24.
    Larese A, Rossi R, Oñate E, Idelsohn SR (2008) Validation of the particle finite element method (pfem) for simulation of free surface flows. Int J Computer-Aided Eng Softw 25:385–425CrossRefzbMATHGoogle Scholar
  25. 25.
    Martin J C, Moyce WJ (1952) Part iv. an experimental study of the collapse of liquid columns on a rigid horizontal plane. Philos Trans R Soc Lond Seri A 244(882):312–324CrossRefGoogle Scholar
  26. 26.
    Oliver X, Cante JC, Weyler R, González C, Hernández J (2007) Particle finite element methods in solid mechanics problems. In: Oñate E, Owen R (eds) Computational Plasticity. Springer, BerlinGoogle Scholar
  27. 27.
    Oliver X, Hartmann S, Cante JC, Weyler R, Hernández J (2009) A contact domain method for large deformation frictional contact problems. part 1: theoretical basis. Comput Methods Appl Mech Eng 198:2591–2606CrossRefzbMATHGoogle Scholar
  28. 28.
    Oñate E, Idelsohn SR, Celigueta A, 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):1777–1800Google Scholar
  29. 29.
    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):1046–1072zbMATHGoogle Scholar
  30. 30.
    Oñate E, Celigueta MA, Idelsohn SR, Salazar F, Suarez B (2011) Possibilities of the particle finite element method for fluid-soil-structure interaction problems. Comput Mech 48:307–318MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Oñate E, Idelsohn SR, Celigueta MA, Rossi R, Marti J, Carbonell JM, Ryzhakov P, Suárez B (2011) Advances in the particle finite element method (pfem) for solving coupled problems in engineering. In: Oñate E, Owen R (eds) Particle-based methods: fundamentals and applications. Springer, Dordrecht, pp 1–49CrossRefGoogle Scholar
  32. 32.
    Oñate E, Marti J, Rossi R, Idelsohn SR (2013) Analysis of the melting, burning and flame spread of polymers with the particle finite element method. Comput Assist Methods EngSci 20:165–184MathSciNetGoogle Scholar
  33. 33.
    Oñate E, Franci A, Carbonell JM (2014) Lagrangian formulation for finite element analysis of quasi-incompressible fluids with reduced mass losses. Int J Numer Methods Fluids 74(10):699–731MathSciNetCrossRefGoogle Scholar
  34. 34.
    Oñate E, Franci A, Carbonell JM (2014) A particle finite element method for analysis of industrial forming processes. Comput Mech 54:85–107MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Pelletier D, Fortin A, Camarero R (1989) Are FEM solutions of incompressible flows really incompressible? (or how simple flows can cause headaches!). Int J Numer Fluids 9:99–112MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Rodriguez JM, Carbonell JM, Cante JC, Oliver X (2016) The particle finite element method (pfem) in thermo-mechanical problems. Int J Numer Methods Eng. doi: 10.1002/nme.5186
  37. 37.
    Ryzhakov P (2016) An axisymetric pfem formulation for bottle forming simulation. Comput Part Mech. doi: 10.1007/s40571-016-0114-7
  38. 38.
    Ryzhakov P, Rossi R, Idelsohn SR, Oñate E (2010) A monolithic lagrangian approach for fluid-structure interaction problems. Comput Mech 46:883–899MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Ryzhakov P, Oñate E, Idelsohn SR (2012) Improving mass conservation in simulation of incompressible flows. Int J Numer Methods Eng 90:1435–1451MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Saalfeld A (1991) In: Delaunay edge refinements, Burnaby, pp 33–36Google Scholar
  41. 41.
    Tang B, Li JF, Wang TS (2009) Some improvements on free surface simulation by the particle finite element method. Int JNumer Methods Fluids 60(9):1032–1054MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Tornberg AN, VanderZee E, Guoy D (2008) Triangulation of simple 3d shapes with well-centred tetrahedra. In Proceedings of the 17th international meshing roundtable, pp 19–35Google Scholar
  43. 43.
    Zhang X, Krabbenhoft K, Pedroso DM, Lyamin AV, Sheng D, Vicente da Silva M, Wang D (2013) Particle finite element analysis of large deformation and granular flow problems. Comput Geotech 54:133–142CrossRefGoogle Scholar
  44. 44.
    Zhu M, Scott MH (2014) Modeling fluid-structure interaction by the particle finite element method in opensees. Comput Struct 132:12–21CrossRefGoogle Scholar
  45. 45.
    Zienkiewicz OC, Taylor RL, Nithiarasu P (2005) The finite element method for fluid dynamics, vol 3, 6th edn. Elsiever, OxfordzbMATHGoogle Scholar

Copyright information

© OWZ 2016

Authors and Affiliations

  1. 1.International Center for Numerical Methods in Engineering (CIMNE)Universitat Politcnica de Catalunya (UPC)BarcelonaSpain
  2. 2.Department of Civil and Environmental EngineeringPolitecnico di MilanoMilanoItaly

Personalised recommendations