Advertisement

Computational Mechanics

, 43:51 | Cite as

Modeling of fluid–structure interactions with the space–time finite elements: contact problems

  • Sunil Sathe
  • Tayfun E. Tezduyar
Original Paper

Abstract

Fluid–structure interaction computations based on interface-tracking (moving-mesh) techniques are often hindered if the structural surfaces come in contact with each other. As the distance between two structural surfaces tends to zero, the fluid mesh in between distorts severely and eventually becomes invalid. Our objective is to develop a technique for modeling problems where the contacting structural surfaces would otherwise inhibit flow modeling or even fluid-mesh update. In this paper, we present our contact tracking technique that detects impending contact and maintains a minimum distance between the contacting structural surfaces. Our Surface-Edge-Node Contact Tracking (SENCT) technique conducts a topologically hierarchical search to detect contact between each node and the elements (“surfaces”), edges and other nodes. To keep the contacting surfaces apart by a small distance, we apply to the contacted nodes penalty forces in SENCT-Force (SENCT-F) and displacement restrictions in SENCT-Displacement (SENCT-D). By keeping a minimum distance between the contacting surfaces, we are able to update the fluid mesh in between and model the flow accurately.

Keywords

Contact algorithm Surface-edge-node contact tracking SENCT Fluid–structure interaction Space–time finite elements 

References

  1. 1.
    Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26: 27–36CrossRefGoogle Scholar
  2. 2.
    Tezduyar TE, Aliabadi SK, Behr M, Mittal S (1994) Massively parallel finite element simulation of compressible and incompressible flows. Comput Methods Appl Mech Eng 119: 157–177zbMATHCrossRefGoogle Scholar
  3. 3.
    Mittal S, Tezduyar TE (1994) Massively parallel finite element computation of incompressible flows involving fluid-body interactions. Comput Methods Appl Mech Eng 112: 253–282zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows—Fluid–structure interactions. Int J Numer Methods Fluids 21: 933–953zbMATHCrossRefGoogle Scholar
  5. 5.
    Johnson AA, Tezduyar TE (1999) Advanced mesh generation and update methods for 3D flow simulations. Comput Mech 23: 130–143zbMATHCrossRefGoogle Scholar
  6. 6.
    Kalro V, Tezduyar TE (2000) A parallel 3D computational method for fluid–structure interactions in parachute systems. Comput Methods Appl Mech Eng 190: 321–332zbMATHCrossRefGoogle Scholar
  7. 7.
    Stein K, Benney R, Kalro V, Tezduyar TE, Leonard J, Accorsi M (2000) Parachute fluid–structure interactions: 3-D Computation. Comput Methods Appl Mech Eng 190: 373–386 zbMATHCrossRefGoogle Scholar
  8. 8.
    Tezduyar T, Osawa Y (2001) Fluid–structure interactions of a parachute crossing the far wake of an aircraft. Comput Methods Appl Mech Eng 191: 717–726zbMATHCrossRefGoogle Scholar
  9. 9.
    Ohayon R (2001) Reduced symmetric models for modal analysis of internal structural-acoustic and hydroelastic-sloshing systems. Comput Methods Appl Mech Eng 190: 3009–3019zbMATHCrossRefGoogle Scholar
  10. 10.
    Tezduyar TE, Sathe S, Keedy R, Stein K (2004) Space–time techniques for finite element computation of flows with moving boundaries and interfaces. In: Gallegos S, Herrera I, Botello S, Zarate F, Ayala G (eds) Proceedings of the III International Congress on Numerical Methods in Engineering and Applied Science. CD-ROM, Monterrey, MexicoGoogle Scholar
  11. 11.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2004) Influence of wall elasticity on image-based blood flow simulation. Jpn Soc Mech Eng J A 70:1224–1231 (in Japanese)Google Scholar
  12. 12.
    van Brummelen EH, de Borst R (2005) On the nonnormality of subiteration for a fluid–structure interaction problem. SIAM J Sci Comput 27: 599–621zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Michler C, van Brummelen EH, de Borst R (2005) An interface Newton–Krylov solver for fluid–structure interaction. Int J Numer Methods Fluids 47: 1189–1195zbMATHCrossRefGoogle Scholar
  14. 14.
    Gerbeau J-F, Vidrascu M, Frey P (2005) Fluid–structure interaction in blood flow on geometries based on medical images. Comput Struct 83: 155–165CrossRefGoogle Scholar
  15. 15.
    Tezduyar TE, Sathe S, Keedy R, Stein K (2006) Space–time finite element techniques for computation of fluid–structure interactions. Comput Methods Appl Mech Eng 195: 2002–2027zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Tezduyar TE, Sathe S, Stein K (2006) Solution techniques for the fully-discretized equations in computation of fluid–structure interactions with the space–time formulations. Comput Methods Appl Mech Eng 195: 5743–5753zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Computer modeling of cardiovascular fluid–structure interactions with the Deforming-Spatial-Domain/Stabilized Space–Time formulation. Comput Methods Appl Mech Eng 195: 1885–1895zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Fluid–structure interaction modeling of aneurysmal conditions with high and normal blood pressures. Comput Mech 38: 482–490CrossRefzbMATHGoogle Scholar
  19. 19.
    Dettmer W, Peric D (2006) A computational framework for fluid–structure interaction: Finite element formulation and applications. Comput Methods Appl Mech Eng 195: 5754–5779zbMATHCrossRefGoogle Scholar
  20. 20.
    Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid–structure interaction analysis with applications to arterial blood flow. Comput Mech 38: 310–322CrossRefMathSciNetzbMATHGoogle Scholar
  21. 21.
    Khurram RA, Masud A (2006) A multiscale/stabilized formulation of the incompressible Navier–Stokes equations for moving boundary flows and fluid–structure interaction. Comput Mech 38: 403–416CrossRefzbMATHGoogle Scholar
  22. 22.
    Kuttler U, Forster C, Wall WA (2006) A solution for the incompressibility dilemma in partitioned fluid–structure interaction with pure Dirichlet fluid domains. Comput Mech 38: 417–429CrossRefGoogle Scholar
  23. 23.
    Lohner R, Cebral JR, Yang C, Baum JD, Mestreau EL, Soto O (2006) Extending the range of applicability of the loose coupling approach for FSI simulations. In: Bungartz H-J, Schafer M (eds) Fluid–structure interaction. Lecture Notes in Computational Science and Engineering, vol 53. Springer, Berlin, pp 82–100Google Scholar
  24. 24.
    Bletzinger K-U, Wuchner R, Kupzok A (2006) Algorithmic treatment of shells and free form-membranes in FSI. In: Bungartz H-J, Schafer M (eds) Fluid–structure interaction. Lecture Notes in Computational Science and Engineering, vol 53. Springer, Berlin, pp 336–355Google Scholar
  25. 25.
    Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Influence of wall elasticity in patient-specific hemodynamic simulations. Comput Fluids 36: 160–168zbMATHCrossRefGoogle Scholar
  26. 26.
    Masud A, Bhanabhagvanwala M, Khurram RA (2007) An adaptive mesh rezoning scheme for moving boundary flows and fluid–structure interaction. Comput Fluids 36: 77–91zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Sawada T, Hisada T (2007) Fuid–structure interaction analysis of the two dimensional flag-in-wind problem by an interface tracking ALE finite element method. Comput Fluids 36: 136–146zbMATHCrossRefGoogle Scholar
  28. 28.
    Wall WA, Genkinger S, Ramm E (2007) A strong coupling partitioned approach for fluid–structure interaction with free surfaces. Comput Fluids 36: 169–183zbMATHCrossRefGoogle Scholar
  29. 29.
    Idelsohn SR, Marti J, Souto-Iglesias A, Onate E (2008) Interaction between an elastic structure and free-surface flows: experimental versus numerical comparisons using the PFEM. Comput Mech, published online. doi: 10.1007/s00466-008-0245-7, February 2008
  30. 30.
    Dettmer WG, Peric D (2008) On the coupling between fluid flow and mesh motion in the modelling of fluid–structure interaction. Comput Mech, published online. doi: 10.1007/s00466-008-0254-6, February 2008
  31. 31.
    Kuttler U, Wall WA (2008) Fixed-point fluid–structure interaction solvers with dynamic relaxation. Comput Mech, published online. doi: 10.1007/s00466-008-0255-5, February 2008
  32. 32.
    Heil M, Hazel AL, Boyle J (2008) Solvers for large-displacement fluid–structure interaction problems: segregated versus monolithic approaches. Comput Mech, published online. doi: 10.1007/s00466-008-0270-6, March 2008
  33. 33.
    Bazilevs Y, Hughes TJR (2008) NURBS-based isogeometric analysis for the computation of flows about rotating components. Comput Mech, published online. doi: 10.1007/s00466-008-0277-z, April 2008
  34. 34.
    Manguoglu M, Sameh AH, Tezduyar TE, Sathe S (2008) A nested iterative scheme for computation of incompressible flows in long domains. Comput Mech, published online. doi: 10.1007/s00466-008-0276-0, April 2008
  35. 35.
    Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) A fully-integrated approach to fluid–structure interaction. Comput Mech (in preparation)Google Scholar
  36. 36.
    Tezduyar TE, Sathe S, Stein K, Aureli L (2006) Modeling of fluid–structure interactions with the space–time techniques. In: Bungartz H-J, Schafer M (eds) Fluid–structure interaction, Lecture Notes in Computational Science and Engineering, vol 53. Springer, Berlin, pp 50–81Google Scholar
  37. 37.
    Tezduyar TE, Sathe S (2007) Modeling of fluid–structure interactions with the space–time finite elements: Solution techniques. Int J Numer Methods Fluids 54: 855–900zbMATHCrossRefMathSciNetGoogle Scholar
  38. 38.
    Tezduyar TE, Sathe S, Cragin T, Nanna B, Conklin BS, Pausewang J, Schwaab M (2007) Modeling of fluid–structure interactions with the space–time finite elements: Arterial fluid mechanics. Int J Numer Methods Fluids 54: 901–922zbMATHCrossRefMathSciNetGoogle Scholar
  39. 39.
    Tezduyar TE, Sathe S, Schwaab M, Conklin BS (2007) Arterial fluid mechanics modeling with the stabilized space–time fluid–structure interaction technique. Int J Numer Methods Fluids, published online. doi: 10.1002/fld.1633, October 2007
  40. 40.
    Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Interface projection techniques for fluid–structure interaction modeling with moving-mesh methods. Comput Mech, published online. doi: 10.1007/s00466-008-0261-7, March 2008
  41. 41.
    Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Fluid–structure interaction modeling of ringsail parachutes. Comput Mech, published online. doi: 10.1007/s00466-008-0260-8, March 2008
  42. 42.
    Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28: 1–44zbMATHMathSciNetCrossRefGoogle Scholar
  43. 43.
    Tezduyar TE, Behr M, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space–time procedure: I. The concept and the preliminary numerical tests. Comput Methods Appl Mech Eng 94: 339–351zbMATHCrossRefMathSciNetGoogle Scholar
  44. 44.
    Tezduyar TE, Behr M, Mittal S, Liou J (1992) 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. Comput Methods Appl Mech Eng 94: 353–371zbMATHCrossRefMathSciNetGoogle Scholar
  45. 45.
    Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43: 555–575zbMATHCrossRefMathSciNetGoogle Scholar
  46. 46.
    Hughes TJR, Brooks AN (1979) A multi-dimensional upwind scheme with no crosswind diffusion. In: Hughes TJR(eds) Finite Element Methods for Convection Dominated Flows, AMD-Vol 34. ASME, New York, pp 19–35Google Scholar
  47. 47.
    Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 32: 199–259zbMATHCrossRefMathSciNetGoogle Scholar
  48. 48.
    Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput Methods Appl Mech Eng 95: 221–242zbMATHCrossRefGoogle Scholar
  49. 49.
    Hughes TJR, Franca LP, Balestra M (1986) A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuška–Brezzi condition: A stable Petrov–Galerkin formulation of the Stokes problem accommodating equal-order interpolations. Comput Methods Appl Mech Eng 59: 85–99zbMATHCrossRefMathSciNetGoogle Scholar
  50. 50.
    Tezduyar TE, Osawa Y (2000) Finite element stabilization parameters computed from element matrices and vectors. Comput Methods Appl Mech Eng 190: 411–430zbMATHCrossRefGoogle Scholar
  51. 51.
    Tezduyar TE (2004) Finite element methods for fluid dynamics with moving boundaries and interfaces. In: Stein E, De Borst R, Hughes TJR (eds) Encyclopedia of Computational Mechanics, vol 3: Fluids, Chap 17. Wiley, New YorkGoogle Scholar
  52. 52.
    Tezduyar TE (2007) Finite elements in fluids: Stabilized formulations and moving boundaries and interfaces. Comput Fluids 36: 191–206CrossRefMathSciNetGoogle Scholar
  53. 53.
    Lo A (1982) Nonlinear dynamic analysis of cable and membrane structure. Ph.D. thesis, Department of Civil Engineering, Oregon State UniversityGoogle Scholar
  54. 54.
    Benney RJ, Stein KR, Leonard JW, Accorsi ML (1997) Current 3-D structural dynamic finite element modeling capabilities. In: Proceedings of AIAA 14th Aerodynamic Decelerator Systems Technology Conference, AIAA Paper 97-1506. San Francisco, CaliforniaGoogle Scholar
  55. 55.
    Tezduyar TE (2003) Stabilized finite element methods for computation of flows with moving boundaries and interfaces. In: Lecture Notes on Finite Element Simulation of Flow Problems (Basic—Advanced Course), Japan Society of Computational Engineering and Sciences, Tokyo, JapanGoogle Scholar
  56. 56.
    Tezduyar TE (2003) Stabilized finite element methods for flows with moving boundaries and interfaces. HERMIS: Int J Comput Math Appl 4: 63–88zbMATHMathSciNetGoogle Scholar
  57. 57.
    Tezduyar TE (2007) Finite elements in fluids: Special methods and enhanced solution techniques. Comput Fluids 36: 207–223CrossRefMathSciNetGoogle Scholar
  58. 58.
    Saad Y, Schultz M (1986) GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7: 856–869zbMATHCrossRefMathSciNetGoogle Scholar
  59. 59.
    Tezduyar TE, Behr M, Mittal S, Johnson AA (1992) Computation of unsteady incompressible flows with the finite element methods—space–time formulations, iterative strategies and massively parallel implementations. In: New methods in transient analysis, PVP-Vol.246/AMD-Vol.143. ASME, New York, pp 7–24Google Scholar
  60. 60.
    Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119: 73–94zbMATHCrossRefGoogle Scholar
  61. 61.
    Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8: 83–130zbMATHCrossRefGoogle Scholar
  62. 62.
    Tezduyar T (2001) Finite element interface-tracking and interface-capturing techniques for flows with moving boundaries and interfaces. In: Proceedings of the ASME Symposium on Fluid-Physics and Heat Transfer for Macro- and Micro-Scale Gas-Liquid and Phase-Change Flows (CD-ROM), ASME Paper IMECE2001/HTD-24206, ASME, New YorkGoogle Scholar
  63. 63.
    Tezduyar TE (2003) Stabilized finite element formulations and interface-tracking and interface-capturing techniques for incompressible flows. In: Hafez MM(eds) Numerical Simulations of Incompressible Flows. World Scientific, New Jersey, pp 221–239Google Scholar
  64. 64.
    Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid–structure interactions with large displacements. J Appl Mech 70: 58–63zbMATHCrossRefGoogle Scholar
  65. 65.
    Tezduyar TE, Sathe S, Senga M, Aureli L, Stein K, Griffin B (2005) Finite element modeling of fluid–structure interactions with space–time and advanced mesh update techniques. In: Proceedings of the 10th International Conference on Numerical Methods in Continuum Mechanics (CD-ROM), Zilina, SlovakiaGoogle Scholar
  66. 66.
    Karypis G, Kumar V (1998) A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J Sci Comput 20: 359–392CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Mechanical EngineeringRice University—MS 321HoustonUSA

Personalised recommendations