Skip to main content
Log in

Flapping and contact FSI computations with the fluid–solid interface-tracking/interface-capturing technique and mesh adaptivity

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

The fluid–solid interface-tracking/interface-capturing technique (FSITICT) with arbitrary Lagrangian–Eulerian interface-tracking and Eulerian interface-capturing is applied to computations of fluid–structure interaction problems with flapping and contact. The two-dimensional model with contacting flaps is intended to represent a valve problem from biomechanics. The FSITICT is complemented with local mesh adaptivity, which significantly increases the performance of the interface-capturing component of the method. The test computations presented demonstrate how our approach works.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25

Similar content being viewed by others

References

  1. Akin JE, Tezduyar T, Ungor M (2007) Computation of flow problems with the mixed interface-tracking/interface-capturing technique (MITICT). Comput Fluids 36:2–11

    Article  MATH  Google Scholar 

  2. Asterino M, Gerbeau JF, Pantz O, Traoré KF (2009) Fluid-structure interaction and multi-body contact: application to aortic valves. Comput Methods Appl Mech Eng 198:3603–3612

    Article  Google Scholar 

  3. Bangerth W, Heister T, Kanschat G (2012) Differential Equations Analysis Library.

  4. Becker R, Rannacher R (1996) A feed-back approach to error control in finite element methods: basic analysis and examples. East-West J Numer Math 4:237–264

    MATH  MathSciNet  Google Scholar 

  5. Belytschko T, Parimi C, Moes N, Sukumar N, Usui S (2003) Structured extended finite element methods for solids defined by implicit surfaces. Int J Numer Methods Eng 56:609–635

    Article  MATH  Google Scholar 

  6. Berenger J (1994) A perfectly matched layer for the absorption of electromagnetic waves. J Comput Phys 114.

  7. Brooks A, Hughes T (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(1–3):199–259

    Article  MATH  MathSciNet  Google Scholar 

  8. Bukac M, Canic S, Glowinski R, Tambaca J, Quaini A (2012) Fluid-structure interaction in blood ow capturing non-zero longitudinal structure displacement. J Comput Phys. http://dx.doi.org/10.1016/j.jcp.2012.08.033

  9. Ciarlet PG (1984) Mathematical elasticity. Volume 1: three dimensional elasticity. North-Holland

  10. Ciarlet PG (1987) The finite element method for elliptic problems, 2. pr. edn. North-Holland, Amsterdam [u.a.].

  11. Cottet GH, Maitre E, Mileent T (2008) Eulerian formulation and level set models for incompressible fluid-structure interaction. Math Model Numer Anal 42:471–492

    Article  MATH  Google Scholar 

  12. Cruchaga M, Celentano D, Tezduyar T (2007) A numerical model based on the mixed interface-tracking/ interface-capturing technique (MITICT). Int J Numer Methods Fluids 54:1021–1030

    Article  MATH  Google Scholar 

  13. Donéa J, Fasoli-Stella P, Giuliani S (1977) Lagrangian and Eulerian finite element techniques for transient fluid-structure interaction problems. In: Trans. 4th Int. Conf. on Structural Mechanics in Reactor Technology, p. Paper B1/2

  14. Dunne T (2006) An Eulerian approach to fluid-structure interaction and goal-oriented mesh adaption. Int J Numer Methods Fluids 51:1017–1039

    Article  MATH  MathSciNet  Google Scholar 

  15. Fernández F, Moubachir M (2005) A Newton method using exact Jacobians for solving fluid-structure coupling. Comput Struct 83:127–142

    Article  Google Scholar 

  16. Formaggia L, Gerbeau JF, Nobile F, Quarteroni A (2001) On the coupling of 3d and 1d Navier-Stokes equations for flow problems in compliant vessels. Comput Methods Appl Mech Eng 191:561–582

    Article  MATH  MathSciNet  Google Scholar 

  17. Formaggia L, Quarteroni A, Veneziani A (2009) Cardiovascular mathematics: modeling and simulation of the circulatory system. Springer, Italia, Milano

    Book  Google Scholar 

  18. Fung Y (1984) Biodynamics: circulation, first ed. edn. Springer, Berlin.

  19. Gazzola F, Squassina M (2006) Global solutions and finite time blow up for damped semilinear wave equations. Ann I H Poincaré 23:185–207

    Article  MATH  MathSciNet  Google Scholar 

  20. Gil AJ, Carreno AA, Bonet J, Hassan O (2010) The immersed structural potential method for haemodynamic applications. J Comput Phys 229:8613–8641

    Article  MATH  MathSciNet  Google Scholar 

  21. Girault V, Raviart PA (1986) Finite element method for the Navier-Stokes equations. Number 5 in computer series in computational mathematics. Springer, Berlin.

  22. He P, Qiao R (2011) A full-Eulerian solid level set method for simulation of fluid-structure interactions. Microfluid Nanofluid 11:557–567

    Article  Google Scholar 

  23. Heywood JG, Rannacher R, Turek S (1996) Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. Int J Numer Methods Fluids 22:325–352

    Article  MATH  MathSciNet  Google Scholar 

  24. Hirt C, Amsden A, Cook J (1974) An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J Comput Phys 14:227–253

    Article  MATH  Google Scholar 

  25. Hughes T, Liu W, Zimmermann T (1981) Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329–349

    Article  MATH  MathSciNet  Google Scholar 

  26. Johnson A, Tezduyar T (1999) Advanced mesh generation and update methods for 3D flow simulations. Comp Mech 23:130–143

    Article  MATH  Google Scholar 

  27. Johnson A, Tezduyar T (2001) Methods for 3D computation of fluid-object interactions in spatially-periodic flows. Comput Methods Appl Mech Eng 190:3201–3221

    Article  MATH  Google Scholar 

  28. Johnson AA, Tezduyar T (1996) 3D simulation of fluid-particle interactions with the number of particles reaching 100. Comput Methods Appl Mech Eng 145:301–321

    Article  MathSciNet  Google Scholar 

  29. Johnson AA, Tezduyar T (1996) Simulation of multiple spheres falling in a liquid-filled tube. Comput Methods Appl Mech Eng 134:351–373

    Article  MATH  MathSciNet  Google Scholar 

  30. Moes N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150

    Article  MATH  Google Scholar 

  31. Moghadam ME, Bazilevs Y, Hsia TY, Vignon-Clementel IE, Marsden AL (2011) A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations. Comput Mech 48:277–291

    Article  MATH  MathSciNet  Google Scholar 

  32. Noh W (1964) A time-dependent two-space-dimensional coupled Eulerian-Lagrangian code, Methods Comput Phys, vol 3, 31st edn. Academic Press, New York

    Google Scholar 

  33. Quarteroni A (2006) What mathematics can do for the simulation of blood circulation. Tech. rep, MOX Institute, Milano

    Google Scholar 

  34. Rannacher R (1986) On the stabilization of the Crank-Nicolson scheme for long time calculations. Preprint

  35. Richter T (2012) A fully Eulerian formulation for fluid-structure interaction problems. J Comput Phys 233:227–240

    Article  Google Scholar 

  36. Richter T, Wick T (2010) Finite elements for fluid-structure interaction in ALE and fully Eulerian coordinates. Comput Methods Appl Mech Eng 199:2633–2642

    Article  MATH  MathSciNet  Google Scholar 

  37. Santos NDD, Gerbeau JF, Bourgat J (2008) A partitioned fluid-structure algorithm for elastic thin valves with contact. Comput Methods Appl Mech Eng 197(19–20):1750–1761

    Article  MATH  Google Scholar 

  38. Sathe S, Tezduyar T (2008) Modeling of fluid-structure interactions with the space-time finite elements: contact problems. Comput Mech 43:51–60

    Article  MATH  MathSciNet  Google Scholar 

  39. Sugiyama K, Li S, Takeuchi S, Takagi S, Matsumato Y (2011) A full Eulerian finite difference approach for solving fluid-structure interacion. J Comput Phys 230:596–627

    Article  MATH  MathSciNet  Google Scholar 

  40. Takagi S, Sugiyama K, Matsumato Y (2012) A review of full Eulerian mehtods for fluid structure interaction problems. J Appl Mech 79(1):010911

    Article  Google Scholar 

  41. Takizawa K, Tezduyar T (2012) Computational methods for parachute fluid-structure interactions. Arch Comput Methods Eng 19:125–169

    Article  MathSciNet  Google Scholar 

  42. Takizawa K, Wright S, Moorman C, Tezduyar T (2011) Fluid-structure interaction modeling of parachute clusters. Int J Numer Methods Fluids 65:286–307

    Article  MATH  Google Scholar 

  43. Takizawa K, Fritze M, Montes D, Spielman T, Tezduyar T (2012) Fluid-structure interaction modeling of ringsail parachutes with disreefing and modified geometric porosity. Comput Mech 50:835–854

    Article  MATH  Google Scholar 

  44. Takizawa K, Henicke B, Puntel A, Kostov N, Tezduyar T (2012) Space-time techiques for computational aerodynamics modeling of flapping wings of an actual locust. Comput Mech 50:743–760

    Article  MATH  Google Scholar 

  45. Takizawa K, Henicke B, Puntel A, Spielman T, Tezduyar T (2012) Space-time techiques for the aerodynamics of flapping wings. J Appl Mech 79:010903

    Article  Google Scholar 

  46. Takizawa K, Kostov N, Puntel A, Henicke B, Tezduyar T (2012) Space-time computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle. Comput Mech 50:761–778

    Article  MATH  Google Scholar 

  47. Takizawa K, Spielman T, Tezduyar T (2011) Space-time FSI modeling and dynamical analysis of spacecraft parachutes and parachute clusters. Comput Mech 48:345–364

    Article  MATH  Google Scholar 

  48. Tezduyar T (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28:1–44

    Article  MATH  MathSciNet  Google Scholar 

  49. Tezduyar T (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8(2):83–130

    Article  MATH  MathSciNet  Google Scholar 

  50. Tezduyar T (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43:555–575

    Article  MATH  MathSciNet  Google Scholar 

  51. Tezduyar T (2006) Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces. Comput Methods Appl Mech Eng 195:2983–3000

    Article  MATH  MathSciNet  Google Scholar 

  52. Tezduyar T, Aliabadi S (2000) EDICT for 3D computation of two-fluid interfaces. Comput Methods Appl Mech Eng 190:403–410

    Article  MATH  Google Scholar 

  53. Tezduyar T, Sathe S (2007) Modeling of fluid-structure interactions with the space-time finite elements: solution techniques. Int J Numer Methods Fluids 54:855–900

    Article  MATH  MathSciNet  Google Scholar 

  54. Tezduyar T, 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 94:339–351

    Article  MATH  MathSciNet  Google Scholar 

  55. Tezduyar T, 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 94:353–371

    Article  MATH  MathSciNet  Google Scholar 

  56. Tezduyar T, Aliabadi S, Behr M (1998) Enhanced-discretization interface-capturing technique (EDICT) for computation of unsteady flows with interfaces. Comput Methods Appl Mech Eng 155:235–248

    Article  MATH  Google Scholar 

  57. Tezduyar T, Sathe S, Keedy R, Stein K (2006) Space-time finite element techniques for computation of fluid-structure interactions. Comput Methods Appl Mech Eng 195:2002–2027

    Article  MATH  MathSciNet  Google Scholar 

  58. Tezduyar T, Sathe S, Stein K (2006) Solution techniques for the fully discretized equations in computation of fluid-structure interaction with space-time formulations. Comput Methods Appl Mech Eng 195(41–43):5743–5753

    Article  MATH  MathSciNet  Google Scholar 

  59. Tezduyar T, Takizawa K, Moorman C, Wright S, Christopher J (2010) Space-time finite element computation of complex fluid-structure interaction. Int J Numer Meth Fluids 64:1201–1218

    Article  MATH  Google Scholar 

  60. Wick T (2011) Adaptive finite element simulation of fluid-structure interaction with application to Heart-Valve Dynamics. Ph.D. thesis, University of Heidelberg

  61. Wick T (2011) Fluid-structure interactions using different mesh motion techniques. Comput Struct 89(13–14):1456–1467

    Article  Google Scholar 

  62. Wick T (2012) Coupling of fully Eulerian with arbitrary Lagrangian-Eulerian coordinates for fluid-structure interaction. Preprint

  63. Wick T (2012) Fully Eulerian fluid-structure interaction for time-dependent problems. Comput Methods Appl Mech Eng 255:14–26. doi:10.1016/j.cma.2012.11.009

    Article  MathSciNet  Google Scholar 

  64. Wick T (2012) Goal-oriented mesh adaptivity for fluid-structure interaction with application to heart-valve settings. Arch Mech Eng 59(6):73–99

    MathSciNet  Google Scholar 

  65. Wick T (2013) Coupling of fully Eulerian and arbitrary Lagrangian-Eulerian methods for fluid-structure interaction computations. Comput Mech. doi:10.1007/s00466-013-0866-3

    MathSciNet  Google Scholar 

  66. Wick T (2013) Solving monolithic fluid-structure interaction problems in arbitrary Lagrangian Eulerian coordinates with the deal.ii library. Arch Numerl Software 1, 1–19. http://www.archnumsoft.org

  67. Zhao H, Freund J, Moser R (2008) A fixed-mesh method for incompressible flow-structure systems with finite solid deformations. J Comput Phys 227(6):3114–3140

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

I thank Prof. R. Rannacher (Heidelberg) and Dr. med. J. Mizerski (Warsaw) for initiating this project during my PhD studies.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Thomas Wick.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wick, T. Flapping and contact FSI computations with the fluid–solid interface-tracking/interface-capturing technique and mesh adaptivity. Comput Mech 53, 29–43 (2014). https://doi.org/10.1007/s00466-013-0890-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-013-0890-3

Keywords

Mathematics Subject Classificaion

Navigation