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The Particle Finite Element Method for Multi-Fluid Flows

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Book cover Particle-Based Methods

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 25))

Abstract

This paper presents the Particle Finite Element Method (PFEM) and its application to multi-fluid flows. Key features of the method are the use of a Lagrangian description to model the motion of the fluid particles (nodes) and that all the information is associated to the particles. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral form, are solved as in the standard FEM.We have extended the method to problems involving several different fluids with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking any kind of interfaces.

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References

  1. Batchelor, G., An Introduction to Fluid Dynamics. Cambridge University Press, 1967.

    Google Scholar 

  2. Caboussat, A., Numerical simulation of two-phase free surface flows. Archives of Computational Methods in Engineering 12:165–224, 2005.

    Article  MATH  Google Scholar 

  3. Carbonell, J., Modeling of ground excavation with the Particle Finite Element Method. Ph.D. Thesis, Universitat Politècnica de Catalunya, Barcelona (Spain), 2009.

    Google Scholar 

  4. Del Pin, F., Idelsohn, S., Oñate, E., Aubry, R., The ALE/Lagrangian Particle Finite Element Method: A new approach to computation of free-surfaces flows and fluid-object interactions. Computers and Fluids 36(1):27–38, 2007.

    Article  MATH  Google Scholar 

  5. Drysdale, D., An Introduction to Fire Dynamics. Wiley Interscience, 1985.

    Google Scholar 

  6. Edelsbrunner, H., Mücke, E., Three-dimensional alpha shapes. ACM Transactions on Graphics 13:43–72, 1994.

    Article  MATH  Google Scholar 

  7. Fernandez-Pello, A., Flame spread modeling. Combustion Science and Technology 39:119–134, 1984.

    Article  Google Scholar 

  8. Gonzalez-Ferrari, C., El Método de los Elementos Finitos de Partículas: Aplicaciones a la pulvimetalurgia industrial. Ph.D. thesis, Universitat Politécnica de Catalunya, 2009.

    Google Scholar 

  9. Harlow, F., The Particle-in-Cell computing method for fluid dynamics. Methods in Computational Physics 3:313–343, 1964.

    Google Scholar 

  10. Hirt, C., Cook, J., Butler, T., A Lagrangian method for calculating the dynamics of an incompressible fluid with free surface. Journal of Computational Physics 5:103–124, 1970.

    Article  MATH  Google Scholar 

  11. Hirt, C., Nichols, B., Volume of Fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 39:201–225, 1981.

    Article  MATH  Google Scholar 

  12. Hughes, T., Liu, W., Zimmermann, T., Lagrangian-Eulerian finite element element formulation for incompressible viscous flows. Computer Methods in Applied Mechanics and Engineering 29:239–349, 1981.

    Article  MathSciNet  Google Scholar 

  13. Idelsohn, S., Calvo, N., Oñate, E., Polyhedrization of an arbitrary 3D point set. Computer Methods in Applied Mechanics and Engineering 192:2649–2667, 2003.

    Article  MATH  Google Scholar 

  14. Idelsohn, S., Del Pin, F., Rossi, R., Oñate, E., Fluid-structure interaction problems with strong added-mass effect. International Journal for Numerical Methods in Engineering 80:1261–1294, 2009.

    Article  MATH  MathSciNet  Google Scholar 

  15. Idelsohn, S., Marti, J., Limache, A., Oñate, E., Unified Lagrangian formulation for elastic solids and incompressible fluids: Application to fluid-structure interaction problems via the PFEM. Computer Methods in Applied Mechanics and Engineering 197:1762–1776, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  16. Idelsohn, S., Marti, J., Souto-Iglesias, A., Oñate, E., Interaction between an elastic structure and free-surface flows: Experimental versus numerical comparisons using the PFEM. Computational Mechanics 43:125–132, 2008.

    Article  MATH  Google Scholar 

  17. Idelsohn, S.,Mier-Torrecilla, M., Nigro, N., Oñate, E., On the analysis of heterogeneous fluids with jumps in the viscosity using a discontinuous pressure field. Computational Mechanics, 2009 (in press).

    Google Scholar 

  18. Idelsohn, S., Mier-Torrecilla, M., Oñate, E., Multi-fluid flows with the Particle Finite Element Method. Computer Methods in Applied Mechanics and Engineering 198:2750–2767, 2009.

    Article  Google Scholar 

  19. Idelsohn, S., Oñate, E., Del Pin, F., A Lagrangian meshless finite element method applied to fluid-structure interaction problems. Computers and Structures 81(8–11), 655–671, 2003.

    Article  Google Scholar 

  20. Idelsohn, S., Oñate, E., Del Pin, F., The Particle Finite Element Method: A powerful tool to solve incompressible flows with free-surfaces and breaking waves. International Journal for Numerical Methods in Engineering 61(7):964–989, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  21. Idelsohn, S., Oñate, E., Del Pin, F., Calvo, N., Fluid-structure interaction using the Particle Finite Element Method. Computer Methods in Applied Mechanics and Engineering 195(17–18):2100–2123, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  22. Idelsohn, S., Storti, M., Oñate, E., Lagrangian formulations to solve free surface incompressible inviscid fluid flows. Computer Methods in Applied Mechanics and Engineering 191(6–7):583–593, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  23. Larese, A., Rossi, R., Oñate, E., Idelsohn, S., Validation of the Particle Finite ElementMethod (PFEM) for simulation of free surface flows. Engineering Computations 25:385–425, 2008.

    Article  Google Scholar 

  24. Mier-Torrecilla,M., Numerical simulation ofmulti-fluid flows with the Particle Finite Element Method. Ph.D. Thesis, Technical University of Catalonia, 2010.

    Google Scholar 

  25. Mier-Torrecilla, M., Geyer, A., Phillips, J., Idelsohn, S., Oñate, E., Numerical simulations of negatively buoyant jets in an immiscible fluid using the Particle Finite Element Method. Journal of Fluid Mechanics, 2010 (submitted).

    Google Scholar 

  26. Mier-Torrecilla, M., Idelsohn, S., Oñate, E., A pressure segregation method for the Lagrangian simulation of interfacial flows. International Journal for Numerical Methods in Fluids, 2010 (submitted).

    Google Scholar 

  27. Oliver, J., Cante, J.,Weyler, R., González, C., Hernández, J., Particle finite element methods in solid mechanics problems. In: Computational Plasticity, Vol. 1, pp. 87–103, Springer Verlag, 2007.

    Google Scholar 

  28. Oñate, E., Idelsohn, S., Celigueta, M., Rossi, R., Advances in the Particle Finite Element Method for the analysis of fluid-multibody interaction and bed erosion in free surface flows. Computer Methods in Applied Mechanics and Engineering 197:1777–1800, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  29. Oñate, E., Idelsohn, S., Del Pin, F., Aubry, R., The Particle Finite Element Method: An overview. International Journal of Computational Methods 1(2):267–307, 2004.

    Article  MATH  Google Scholar 

  30. Oñate, E., Rossi, R., Idelsohn, S., Butler, K., Melting and spread of polymers in fire with the Particle Finite Element Method. International Journal for Numerical Methods in Engineering 81:1046–1072, 2009.

    Google Scholar 

  31. Osher, S., Sethian, J., Fronts propagating with curvature dependant speed: algorithms based on Hamilton–Jacobi formulations. Journal of Computational Physics 79:12–49, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  32. Poinsot, T., Veynante, D., Theorical and Numerical Combustion. Edwards, 2001.

    Google Scholar 

  33. Ramaswamy, B., Kawahara, M., Arbitrary Lagrangian-Eulerian finite element method for the analysis of free surface fluid flows. Computational Mechanics 1:103–108, 1986.

    Google Scholar 

  34. Ramaswamy, B., Kawahara, M., Lagrangian finite element analysis applied to viscous free surface fluid flow. International Journal for Numerical Methods in Fluids 7:953–984, 1987.

    Article  MATH  Google Scholar 

  35. Rossi, R., Ryzhakov, P., Oñate, E., A monolithic FE formulation for the analysis of membranes in fluids. International Journal of Space Structures 24:205–210, 2009.

    Article  Google Scholar 

  36. Scardovelli, R., Zaleski, S., Direct Numerical Simulation of free-surface and interfacial flow. Annual Reviews of Fluid Mechanics 31:567–603, 1999.

    Article  MathSciNet  Google Scholar 

  37. Shyy, W., Computational Fluid Dynamics with Moving Boundaries. Taylor & Francis, 1996.

    Google Scholar 

  38. Tezduyar, T., Behr, M., Liou, J., A new strategy for finite element computations involving moving boundaries and interfaces. The deforming-spatial-domain/space-time procedure: I. The concept and preliminary numerical tests. Computer Methods in Applied Mechanics and Engineering 94:339–351, 1992.

    MATH  MathSciNet  Google Scholar 

  39. Tezduyar, T., Behr, M., Mittal, S., Liou, J., A new strategy for finite element computations involving moving boundaries and interfaces. The deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows and flows with drifting cylinders. Computer Methods in Applied Mechanics and Engineering 94:353–371, 1992.

    Google Scholar 

  40. Unverdi, S., Tryggvason, G., Computations of multi-fluid flows. Physica D: Nonlinear Phenomena 60:70–83, 1992.

    Article  MATH  Google Scholar 

  41. Unverdi, S., Tryggvason, G., A front-tracking method for viscous, incompressible, multi-fluid flows. Journal of Computational Physics 100:25–37, 1992.

    Article  MATH  Google Scholar 

  42. Xie, W., DesJardin, P., An embedded upward flame spread model using 2D direct numerical simulations. Combustion and Flame 156:522–530, 2009.

    Article  Google Scholar 

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Correspondence to S. R. Idelsohn .

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Idelsohn, S.R., Mier-Torrecilla, M., Marti, J., Oñate, E. (2011). The Particle Finite Element Method for Multi-Fluid Flows. In: Oñate, E., Owen, R. (eds) Particle-Based Methods. Computational Methods in Applied Sciences, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0735-1_5

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  • DOI: https://doi.org/10.1007/978-94-007-0735-1_5

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  • Online ISBN: 978-94-007-0735-1

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