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Unified Lagrangian Formulation for Fluid and Solid Mechanics, Fluid-Structure Interaction and Coupled Thermal Problems Using the PFEM

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Abstract

The objective of this work is to develop a unified formulation for the solution of fluid and solid mechanics, Fluid-Structure Interaction (FSI) and thermal coupled problems and to prove its efficacy by solving both academic and industrial problems.

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References

  1. S.R. Idelsohn, J. Marti, A. Limache, and E. Oñate. Unified lagrangian formulation for elastic solids and incompressible fluids: Applications to fluid-structure interaction problems via the pfem. Computer Methods In Applied Mechanics And Engineering, 197:1762–1776, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  2. E. Oñate, S.R. Idelsohn, F. Del Pin, and R. Aubry. The particle finite element method. an overview. International Journal for Computational Methods, 1:267–307, 2004.

    MATH  Google Scholar 

  3. O.C. Zienkiewicz and R.L. Taylor. The Finite Element Method. Its Basis and Fundamentals. (6th Ed.). Elsevier Butterworth-Heinemann, Oxford, 2005.

    Google Scholar 

  4. E. Oñate, A. Franci, and J.M. Carbonell. Lagrangian formulation for finite element analysis of quasi-incompressible fluids with reduced mass losses. International Journal for Numerical Methods in Fluids, 74 (10):699–731, 2014.

    Article  MathSciNet  Google Scholar 

  5. A. Franci, E. Oñate, and J. M. Carbonell. Velocity-based formulations for standard and quasi-incompressible hypoelastic-plastic solids. International Journal for Numerical Methods in Engineering, doi:10.1002/nme.5205, 2016.

  6. F. H. Harlow and J. E. Welch. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Physics of Fluids, 8:2182, 1965.

    Article  MATH  Google Scholar 

  7. C.W. Hirt and B.D. Nichols. Volume of fluid (vof) method for the dynamics of free boundaries. Computational Physics, 39:201–225, 1981.

    Article  MATH  Google Scholar 

  8. S.J. Osher and R.P. Fedkiw. Level Set Methods and Dynamic Implicit Surfaces. Springer edition, 2006.

    Google Scholar 

  9. R. Rossi, A. Larese, P. Dadvand, and E. Oñate. An efficient edge-based level set finite element method for free surface flow problems. International Journal for Numerical Methods in Fluids, 71 (6):687–716, 2013.

    Article  MathSciNet  Google Scholar 

  10. P. Becker, S.R. Idelsohn, and E. Oñate. A unified monolithic approach for multi-fluid flows and fluid-structure interaction using the particle finite element method with fixed mesh. Computational Mechanics, 61:1–14, 2015.

    MathSciNet  MATH  Google Scholar 

  11. O.C. Zienkiewicz, R.L. Taylor, and P. Nithiarasu. The Finite Element Method for Fluid Dynamics,Volume 3 (6th Ed.). Elsiever, Oxford, 2005.

    Google Scholar 

  12. J. Donea and A. Huerta. Finite Element Methods for Flow Problems. Wiley, 2003.

    Google Scholar 

  13. M. Chiumenti, M. Cervera, C. Agelet de Saracibar, and N Dialami. Numerical modeling of friction stir welding processes. Computer methods in applied mechanics and engineering, 254:353–369, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  14. S. Tanaka and K. Kashiyama. Ale finite element method for fsi problems with free surface using mesh re-generation method based on background mesh. International Journal of Computational Fluid Dynamics, 20:229–236, 2006.

    Article  MATH  Google Scholar 

  15. S.R. Idelsohn, E. Oñate, and F. Del Pin. 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, 61:964–989, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  16. PFEM in CIMNE website. www.cimne.com/pfem.

  17. A. Larese, R. Rossi, E. Oñate, and S.R. Idelsohn. Validation of the particle finite element method (pfem) for simulation of free surface flows. International Journal for Computer-Aided Engineering and Software, 25:385–425, 2008.

    Article  MATH  Google Scholar 

  18. M. Cremonesi, L. Ferrara, A. Frangi, and U. Perego. A lagrangian finite element approach for the simulation of water-waves induced by landslides. Computer and Structures, 89:1086–1093, 2011.

    Article  Google Scholar 

  19. B. Tang, J.F. Li, and T.S. Wang. Some improvements on free surface simulation by the particle finite element method. International Journal for Numerical Methods in Fluids, 60 (9):1032–1054, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  20. R. Aubry, S. R. Idelsohn, and E. Oñate. Particle finite element method in fluid-mechanics including thermal convection-diffusion. Computers and Structures, 83:1459–1475, 2005.

    Article  Google Scholar 

  21. E. Oñate, R. Rossi, S.R. Idelsohn, and K. Butler. Melting and spread of polymers in fire with the particle finite element method. International Journal of Numerical Methods in Engineering, 81 (8):1046–1072, 2010.

    MATH  Google Scholar 

  22. E. Oñate, M.A. Celigueta, and S.R. Idelsohn. Modeling bed erosion in free surface flows by th particle finite element method. Acta Geotechnia, 1 (4):237–252, 2006.

    Article  Google Scholar 

  23. S.R. Idelsohn, J. Marti, P. Becker, and E. Oñate. Analysis of multifluid flows with large time steps using the particle finite element method. International Journal for Numerical Methods in Engineering, 75 (9):621–644, 2014.

    Article  MathSciNet  Google Scholar 

  24. T.S. Dang and G. Meschke. An ale-pfem method for the numerical simuation of two-phase mixture flow. Computer Methods in Applied Mechanics and Engineering, 278:599–620, 2014.

    Article  MathSciNet  Google Scholar 

  25. X. Zhang, K. Krabbenhoft, and D. Sheng. Particle finite element analysis of the granular column collapse problem. Granular Matter, 16:609–619, 2014.

    Article  Google Scholar 

  26. E. Oñate, S.R. Idelsohn, M.A. Celigueta, and R. Rossi. 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 (19–20):1777–1800, 2008.

    Google Scholar 

  27. E. Oñate, M.A. Celigueta, S.R. Idelsohn, F. Salazar, and B. Suarez. Possibilities of the particle finite element method for fluid-soil-structure interaction problems. Computation mechanics, 48:307–318, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  28. M. Zhu and M. H. Scott. Modeling fluid-structure interaction by the particle finite element method in opensees. Computers and Structures, 132:12–21, 2014.

    Article  Google Scholar 

  29. J.M. Carbonell, E. Oñate, and B. Suarez. Modeling of ground excavation with the particle finite-element method. Journal of Engineering Mechanics, 136:455–463, 2010.

    Article  Google Scholar 

  30. R.A. Gingold and J.J. Monaghan. Smoothed particle hydrodynamics - theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society, 20:375–389, 1977.

    Article  MATH  Google Scholar 

  31. L. Lucy. A numerical approach to the testing of the fission hypothesis. Astronomical Journal, 82:1013–1024, 1977.

    Article  Google Scholar 

  32. C. Antoci, M. Gallati, and S. Sibilla. A numerical approach to the testing of the fission hypothesis. Computers and Structures, 85:879–890, 2007.

    Article  Google Scholar 

  33. F. Brezzi. 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):129–151, 1974.

    Google Scholar 

  34. J. Von Neumann and R. D. Richtmyer. A method for the numerical calculation of hydrodynamical shoks. Journal of Applied Physics International Journal of Computational Fluid Dynamics, 21:232, 1950.

    MATH  Google Scholar 

  35. T.J.R. Huges and A.N. Brooks. A multi-dimensional upwind scheme with no crosswind diffusion in: Fem for convection dominated flows. 1979.

    Google Scholar 

  36. T.J.R. Hughes, L.P. Franca, and G.M. Hulbert. A new finite element formulation for computational fluid dynamics: Viii. the galerkin/least squares method for advective-diffusive equations. Computer Methods in Applied Mechanics and Engineering, 73 (2), 1989.

    Google Scholar 

  37. T.J.R. Hughes. Multiscale phenomena: Green’s functions, the dirichlet-neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods. Computer Methods in Applied Mechanics and Engineering, 127 (1–4):387–401, 1995.

    Google Scholar 

  38. R. Codina. A stabilized finite element method for generalized stationary incompressible flows. Computer Methods in Applied Mechanics and Engineering, 190 (20–21):2681–2706, 2001.

    Google Scholar 

  39. R. Codina. Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods. Computer Methods in Applied Mechanics and Engineering, 190 (13–14):1579–1599, 2000.

    Google Scholar 

  40. E. Oñate. A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation. Computer Methods in Applied Mechanics and Engineering, 190 (20–21):355–370, 2000.

    Google Scholar 

  41. E. Oñate. Derivation of stabilized equations for advective-diffusive transport and fluid flow problems. Computer methods in applied mechanics and engineering, 151:233–267, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  42. E. Oñate and J. García. A finite element method for fluid-structure interaction with surface waves using a finite calculus formulation. Computer methods in applied mechanics and engineering, 191:635–660, 2001.

    Article  MATH  Google Scholar 

  43. E. Oñate, J. Garcí a, S.R. Idelsohn, and F. Del Pin. Fic formulations for finite element analysis of incompressible flows. eulerian, ale and lagrangian approaches. Computer methods in applied mechanics and engineering, 195 (23–24):3001–3037, 2006.

    Google Scholar 

  44. E. Oñate and M. Manzán. A general procedure for deriving stabilized space-time finite element methods for advective-diffusive problems. International Journal of Numerical Methods in Fluids, 31:202–221, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  45. M. Cervera, M. Chiumenti, and R. Codina. Mixed stabilized finite element methods in nonlinear solid mechanics: Part i: Formulation. Computer Methods In Applied Mechanics And Engineering, 199:2559–2570, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  46. M. Chiumenti, M. Cervera, and R. Codina. Mixed three-field fe formulation for stress accurate analysis including the incompressible limit. Computer Methods In Applied Mechanics And Engineering, 283:1095–1116, 2015.

    Article  MathSciNet  Google Scholar 

  47. M. Chiumenti, Q. Valverde, C. Agelet De Saracibar, and M.Cervera. A stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations. Computer Methods In Applied Mechanics And Engineering, 191:5253–5264, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  48. A.J. Gil, C.H. Lee, J. Bonet, and M. Aguirre. A stabilised petrov-galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics. Computer Methods In Applied Mechanics And Engineering, 276:659–690, 2014.

    Article  MathSciNet  Google Scholar 

  49. A.J. Gil, C.H. Lee, J. Bonet, and M. Aguirre. Development of a stabilised petrov-galerkin formulation for conservation laws in lagrangian fast solid dynamics. Computer Methods In Applied Mechanics And Engineering, 268:40–64, 2014.

    Article  MathSciNet  MATH  Google Scholar 

  50. J. Rojek, E. Oñate, and R.L. Taylor. Cbs-based stabilization in explicit dynamics. International Journal For Numerical Methods In Engineering, 66:1547–1568, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  51. E. Oñate, J. Rojek, R.L. Taylor, and O.C. Zienkiewicz. Finite calculus formulation for incompressble solids using linear triangles and tetrahedra. International Journal For Numerical Methods In Engineering, 59:1473–1500, 2004.

    Google Scholar 

  52. B. Hubner, E. Walhorn, and D.Dinkler. A monolithic approach to fluid-structure interaction using space-time finite elements. Computer Methods in Applied Mechanics and Engineering, 193:2087–2104, 2004.

    Article  MATH  Google Scholar 

  53. C. Michler, S.J. Hulshoff, and E.H. Van Brummelenand R. De Borst. A monolithic approach to fluid-structure interaction. Computers and Fluids, 33:839–848, 2004.

    Article  MATH  Google Scholar 

  54. C.A. Felippa and K.C. Park. Staggered transient analysis procedures for coupled mechanical systems: Formulation. Computer Methods in Applied Mechanics and Engineering, 24:61–111, 1980.

    Article  MATH  Google Scholar 

  55. M. Cremonesi, A. Frangi, and U. Perego. A lagrangian finite element approach for the analysis of fluid-structure interaction problems. International Journal of Numerical Methods in Engineering, 84:610–630, 2010.

    MathSciNet  MATH  Google Scholar 

  56. F. Casadei and S. Potapov. Permanent fluid-structure interaction with non-conforming interfaces in fast transient dynamics. Computer Methods in Applied Mechanics and Engineering, 193:4157–4194, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  57. C.S. Peskin. Flow patterns around hearth values: a numerical method. Journal of Computational Physics, 10:252–271, 1972.

    Article  MathSciNet  MATH  Google Scholar 

  58. A.M. Roma, C.S. Peskin, and M.J. Berger. An adaptative version of the immersed boundary method. Journal of Computational Physics, 153 (2):509–534, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  59. A.J. Gil, A. Arranz Carreño, J. Bonet, and O.Hassan. The immersed structural potential method for haemodynamic applications. Journal of Computational Physics, 229:8613–8641, 2010.

    Article  MathSciNet  Google Scholar 

  60. L. Zhang, A. Gerstenberger, X. Wang, and W.K Liu. Immersed finite element method. Computer Methods In Applied Mechanics And Engineering, 193:2051–2067, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  61. C. Hesch, A.J. Gil, A. Arranz Carreño, and J. Bonet. On continuum immersed strategies for fluid-structure interaction. Computer Methods in Applied Mechanics and Engineering, 247:51–64, 2012.

    Article  MathSciNet  Google Scholar 

  62. F. Brezzi and M. Fortin. Mixed And Hybrid Finite Element Methods. Springer, New York, 1991.

    Book  MATH  Google Scholar 

  63. M. Cervera, M. Chiumenti, L.Benedetti, and R. Codina. Mixed stabilized finite element methods in nonlinear solid mechanics: Part i: Formulation. Computer Methods In Applied Mechanics And Engineering, 285:752–775, 2015.

    Article  MathSciNet  Google Scholar 

  64. P. Ryzhakov, R. Rossi, S.R. Idelsohn, and E. Oñate. A monolithic lagrangian approach for fluid-structure interaction problems. Computational Mechanics, 46:883–899, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  65. H. Edelsbrunner and E.P. Mucke. Three dimensional alpha shapes. ACM Trans Graphics, 13:43–72, 1999.

    Google Scholar 

  66. E. Oñate and J.M. Carbonell. Updated lagrangian finite element formulation for quasi and fully incompressible fluids. Computational Mechanics, 54 (6), 2014.

    Google Scholar 

  67. P. Ryzhakov, E. Oñate, and S.R. Idelsohn. Improving mass conservation in simulation of incompressible flows. International Journal of Numerical Methods in Engineering, 90:1435–1451, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  68. P. Ryzhakov, J. Cotela, R. Rossi, and E. Oñate. A two-step monolithic method for the efficient simulation of incompressible flows. International Journal for Numerical Methods in Fluids, 74 (12):919–934, 2014.

    Article  MathSciNet  Google Scholar 

  69. M. Benzi, G.H. Golub, and J. Liesen. Numerical solution of saddle point problems. Acta Numerica, 14 (1):1–137, 2005.

    Article  MathSciNet  MATH  Google Scholar 

  70. M. Benzi, M.A. Olshanskii, and Z. Wang. Modified augmented lagrangian preconditions for the incompressible navier-stokes equations. International Journal for Numerical Methods in Fluids, 66:486–508, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  71. H.C. Elman, D.J. Silvester, and A.J. Wathen. Finite element and fast iterative solvers with applications in incompressible fluid dynamics. Oxford Series in Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford, 2005.

    MATH  Google Scholar 

  72. M. Fortin and R. Glowinski. Augmented lagrangian: application to the numerical solution of boundary value problems. North-Holland, Amsterdam, 1983.

    MATH  Google Scholar 

  73. S. Vincent, Al Sarthou, J.P. Caltagirone, F. Sonilhac, P. Février, C. Mignot, and G. Pianet. Augmented lagrangian and penalty methods for the simulation of two-phase flows interacting with moving solids. application to hydroplanning flows interacting real tire tread patterns. Journal of Computational Physics, 203 (4):956–983, 2013.

    MathSciNet  Google Scholar 

  74. D. Bresch, E.D. Fernández Nieto, I.R. Ionescu, and P. Vigneaux. Augmented lagrangian method and compressible visco-plastic flow. applications to shallow dense avalanches. New Directions in Mathematical Fluid Mechanics. The Alexander V. Kazhikhov Memorial Volume. In the Series of Book on Advances in Mathematical Fluid Mechanics. A.V. Fursikov, G.P. Galdi and V.V. Pukhnachev (Eds.), Birkhauser Verlag Basel, pages 57–89, 2010.

    Google Scholar 

  75. G. Vinay, A. Wachs, and J.F. Agassant. Numerical simulation of weakly compressible bingham flows: The restart of pipeline flows of waxy crude oil. Journal of Non-Newtonian Fluids Mechanics, 136 (2–3):93–105, 2006.

    Google Scholar 

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Authors and Affiliations

  1. Universitat Politècnica de Catalunya, Barcelona, Spain

    Alessandro Franci

  2. CIMNE, Barcelona, Spain

    Alessandro Franci

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  1. Alessandro Franci
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Franci, A. (2017). Introduction. In: Unified Lagrangian Formulation for Fluid and Solid Mechanics, Fluid-Structure Interaction and Coupled Thermal Problems Using the PFEM. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-45662-1_1

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  • DOI: https://doi.org/10.1007/978-3-319-45662-1_1

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  • Online ISBN: 978-3-319-45662-1

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