Skip to main content
SpringerLink
Log in

FSI modeling with the DSD/SST method for the fluid and finite difference method for the structure

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

Abstract

We present a fluid–structure interaction (FSI) modeling method based on using the deforming-spatial-domain/stabilized space–time (DSD/SST) method for the fluid mechanics part and a finite difference (FD) method for the structural mechanics part. As the structural mechanics model, we focus on the thin-shell model. The fluid mechanics equations with moving boundaries are solved with the DSD/SST method and the thin-shell structural mechanics equation is solved with a FD method, with partitioned coupling between the two parts. The coupling of the DSD/SST and FD solvers makes sure that the boundary conditions on the fluid-structure interface at the end of each time step are matched between the fluid and the structure. A hanging plate in vacuum under gravitational force is performed to validate the structure solver. In addition, a pitching plate in a uniform flow is simulated to validate the FSI solver. The present results are in reasonable agreement with data predicted by other methods.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Peskin CS (1972) Flow patterns around heart valves a digital computer method for solving the equations of motion. Ph.D. thesis, Yeshiva University

  2. Peskin CS (1977) Numerical analysis of blood flow in the heart. J Comput Phys 25:220–252

    Article  MathSciNet  MATH  Google Scholar 

  3. Griffith BE, Hornung RD, McQueen DM, Peskin CS (2007) An adaptive, formally second order accurate version of the immersed boundary method. J Comput Phys 223:10–49

    Article  MathSciNet  MATH  Google Scholar 

  4. Ghias R, Mittal R, Dong H (2007) A sharp interface immersed boundary method for compressible viscous flows. J Comput Phys 225:528–553

    Article  MathSciNet  MATH  Google Scholar 

  5. Kim Y, Peskin CS (2007) Penalty immersed boundary method for an elastic boundary with mass. Phys Fluids 19:053103

    Article  Google Scholar 

  6. Tian FB, Luo H, Zhu L, Lu XY (2010) Interaction between a flexible filament and a downstream rigid body. Phys Rev E 82: 026301

    Google Scholar 

  7. Tian FB, Luo H, Zhu L, Liao JC, Lu XY (2011) An immersed boundary-lattice Boltzmann method for elastic boundaries with mass. J Comput Phys 230:7266–7283

    Article  MathSciNet  MATH  Google Scholar 

  8. Tian FB, Luo H, Zhu L, Lu XY (2011) Coupling modes of three filaments in side-by-side arrangement. Phys Fluids 23:111903

    Article  Google Scholar 

  9. Tian FB (2013) Role of mass on the stability of flag/flags in uniform flow. Appl Phys Lett 103:034101

    Article  Google Scholar 

  10. Xu YQ, Tian FB, Deng YL (2013) An efficient red blood cell model in the frame of IB-LBM and its application. Int J Biomath 6:1250061

    Article  MathSciNet  Google Scholar 

  11. Kim J, Kim D, Choi H (2001) An immersed-boundary finite-volume method for simulations of flow in complex geometries. J Comput Phys 171:132–150

    Article  MathSciNet  MATH  Google Scholar 

  12. Seo JH, Mittal R (2011) A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations. J Comput Phys 230:7347–7363

    Article  MathSciNet  MATH  Google Scholar 

  13. Luo H, Dai H, Ferreira de Sousa P, Yin B (2012) On the numerical oscillation of the direct-forcing immersed-boundary method for moving boundaries. Comput Fluids 56:61–76

    Article  MathSciNet  Google Scholar 

  14. Tian FB, Dai H, Luo H, Doyle JF, Rousseau B (2014) Fluid–structure interaction involving large deformations: 3D simulations and applications to biological systems. J Comput Phys 258:451–469

    Article  MathSciNet  Google Scholar 

  15. Mittal R, Iaccarino G (2005) Immersed boundary method. Annu Rev Fluid Mech 37:239–261

    Article  MathSciNet  Google Scholar 

  16. Hirt CW, Amsden AA, Cook JL (1974) An arbitrary Lagrangian–Eulerian computing method for all flow speeds. J Comput Phys 14:227–253

    Article  MATH  Google Scholar 

  17. Mittal S, Tezduyar T (1992) A finite element study of incompressible flows past oscillating cylinders and airfoils. Int J Numer Methods Fluids 15:1073–1118

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  19. 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 94:353–371

    Article  MathSciNet  MATH  Google Scholar 

  20. 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 94:339–351

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  22. 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 195:2002–2027

    Article  MathSciNet  MATH  Google Scholar 

  23. 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 195:5743–5753

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  25. Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids 36:191–206

    Article  MathSciNet  MATH  Google Scholar 

  26. Wang SY, Tian FB, Jia LB, Lu XY, Yin XZ (2010) The secondary vortex street in the wake of two tandem circular cylinders at low Reynolds number. Phys Rev E 81:036305

    Article  Google Scholar 

  27. Takizawa K, Tezduyar TE (2011) Multiscale space-time fluid–structure interaction techniques. Comput Mech 48:247–267

    Article  MathSciNet  MATH  Google Scholar 

  28. Takizawa K, Tezduyar TE (2012) Space-time fluid–structure interaction methods. Math Models Methods Appl Sci 22(supp02):1230001

    Article  MathSciNet  Google Scholar 

  29. Tian FB, Lu XY, Luo H (2012) Propulsive performance of a body with a traveling wave surface. Phys Rev E 86:016304

    Article  Google Scholar 

  30. Bazilevs Y, Takizawa K, Tezduyar TE (2013) Challenges and directions in computational fluid–structure interaction. Math Models Methods Appl Sci 23:215–221

    Article  MathSciNet  MATH  Google Scholar 

  31. 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 32:199–259

    Article  MathSciNet  MATH  Google Scholar 

  32. Hughes TJR, Tezduyar TE (1984) Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Comput Methods Appl Mech Eng 85:217–284

    Article  MathSciNet  Google Scholar 

  33. 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 95:221–242

    Article  MATH  Google Scholar 

  34. Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows-fluid–structure interactions. Int J Numer Methods Fluids 21:933–953

    Article  MATH  Google Scholar 

  35. Johnson AA, Tezduyar TE (1999) Advanced mesh generation and update methods for 3D flow simulations. Comput Mech 23:130–143

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  37. Takizawa K, Kostov N, Puntel A, Henicke B, Tezduyar TE (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 

  38. Takizawa K, Henicke B, Puntel A, Kostov N, Tezduyar TE (2013) Computer modeling techniques for flapping-wing aerodynamics of a locust. Comput Fluids 85:125–134

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  40. Kalro V, Aliabadi S, Garrard W, Tezduyar T, Mittal S, Stein K (1997) Parallel finite element simulation of large ram-air parachutes. Int J Numer Methods Fluids 24:1353–1369

    Article  MATH  Google Scholar 

  41. 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 43:39–49

    Article  MATH  Google Scholar 

  42. Tezduyar TE, Sathe S, Schwaab M, Pausewang J, Christopher J, Crabtree J (2008) Fluid–structure interaction modeling of ringsail parachutes. Comput Mech 43:133–142

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  46. Takizawa K, Spielman T, Moorman C, Tezduyar TE (2012) Fluid–structure interaction modeling of spacecraft parachutes for simulation-based design. J Appl Mech 79:010907

    Article  Google Scholar 

  47. Takizawa K, Montes D, Fritze M, McIntyre S, Boben J, Tezduyar TE (2013) Methods for FSI modeling of spacecraft parachute dynamics and cover separation. Math Models Methods Appl Sci 23:307–338

    Article  MathSciNet  MATH  Google Scholar 

  48. Tezduyar TE, Takizawa K, Brummer T, Chen PR (2011) Space-time fluid–structure interaction modeling of patient-specific cerebral aneurysms. Int J Numer Methods Biomed Eng 27:1665–1710

    Article  MathSciNet  MATH  Google Scholar 

  49. Takizawa K, Bazilevs Y, Tezduyar TE (2012) Space-time and ALE-VMS techniques for patient-specific cardiovascular fluid–structure interaction modeling. Arch Comput Methods Eng 19:171–225

    Article  MathSciNet  Google Scholar 

  50. Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2012) Patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent. Comput Mech 50:675–686

    Article  MathSciNet  MATH  Google Scholar 

  51. Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2013) Patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms. Comput Mech 51:1061–1073

    Article  MathSciNet  MATH  Google Scholar 

  52. Takizawa K, Henicke B, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48:333–344

    Article  MATH  Google Scholar 

  53. Takizawa K, Henicke B, Montes D, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Numerical-performance studies for the stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48:647–657

    Article  MATH  Google Scholar 

  54. Bazilevs Y, Hsu M-C, Takizawa K, Tezduyar TE (2012) ALE-VMS and ST-VMS methods for computer modeling of wind-turbine rotor aerodynamics and fluid–structure interaction. Math Models Methods Appl Sci 22(supp02):1230002

    Article  Google Scholar 

  55. Tian FB, Bharti RP, Xu YQ (2014) Deforming-spatial-domain/stabilized space–time (DSD/SST) method in computation of non-Newtonian fluid flow and heat transfer with moving boundaries. Comput Mech 53:257–271

    Article  MathSciNet  MATH  Google Scholar 

  56. Deng HB, Xu YQ, Chen DD, Dai H, Wu J, Tian FB (2013) On numerical modeling of animal swimming and flight. Comput Mech 52:1221–1242

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  58. Zhu L, Peskin CS (2002) Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method. J Comput Phys 179:452–468

    Article  MathSciNet  MATH  Google Scholar 

  59. Connell BSH, Yue DKP (2007) Flapping dynamics of a flag in a uniform stream. J Fluid Mech 581:33–67

    Article  MathSciNet  MATH  Google Scholar 

  60. 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

    Article  MATH  Google Scholar 

  61. Stein K, Benney R, Tezduyar T, Potvin J (2001) Fluid-structure interactions of a cross parachute: numerical simulation. Comput Methods Appl Mech Eng 191:673–687

    Article  MATH  Google Scholar 

  62. Stein KR, Benney RJ, Tezduyar TE, Leonard JW, Accorsi ML (2001) Fluid–structure interactions of a round parachute: modeling and simulation techniques. J Aircr 38:800–808

    Article  Google Scholar 

  63. Stein K, Tezduyar T, Kumar V, Sathe S, Benney R, Thornburg E, Kyle C, Nonoshita T (2003) Aerodynamic interactions between parachute canopies. J Appl Mech 70:50–57

    Google Scholar 

  64. Zheng X, Xue Q, Mittal R, Beilamowicz S (2010) A coupled sharp-interface immersed-boundary-finite element method for flow–structure interaction with application to human phonation. J Biomech Eng 132:111003

    Google Scholar 

  65. Tian FB, Lu XY, Luo H (2012) Onset of instability of a flag in uniform flow. Theor Appl Mech Lett 2:022005

    Google Scholar 

  66. Tian FB, Luo H, Song J, Lu XY (2013) Force production and asymmetric deformation of a flexible flapping wing in forward flight. J Fluids Struct 36:149–161

    Article  Google Scholar 

  67. Tian FB, Chang S, Luo H, Rousseau B (2013) A 3D numerical simulation of wave propagation on the vocal fold surface. In: Proceedings of the 10th international conference on advances in quantitative laryngology, voice and speech research. Cincinnati, Ohio, p 94921483

  68. Tian FB, Dai H, Luo H, Doyle JF, Rousseau B (2013) Computational fluid–structure interaction for biological and biomedical flows. In: Proceedings of the ASME 2013 fluids engineering division summer meeting. Incline Village, Nevada, p 16408

  69. Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite element computation of 3D flows. Computer 26:27–36

    Article  Google Scholar 

  70. Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interface. Comput Methods Appl Mech Eng 119:73–94

    Article  MATH  Google Scholar 

  71. Behr M, Tezduyar T (1999) The shear-slip mesh update method. Comput Methods Appl Mech Eng 174:261–274

    Article  MATH  Google Scholar 

  72. Behr M, Tezduyar T (2001) Shear-slip mesh update in 3D computation of complex flow problems with rotating mechanical components. Comput Methods Appl Mech Eng 190:3189–3200

    Article  MATH  Google Scholar 

  73. Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid–structure interactions with large displacements. J Appl Mech 70:58–63

    Article  MATH  Google Scholar 

  74. Stein K, Tezduyar TE, Benney R (2004) Automatic mesh update with the solid-extension mesh moving technique. Comput Methods Appl Mech Eng 193:2019–2032

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  77. Johnson AA, Tezduyar TE (1997) Parallel computation of incompressible flows with complex geometries. Int J Numer Methods Fluids 24:1321–1340

    Article  MATH  Google Scholar 

  78. Johnson AA, Tezduyar TE (1997) 3D simulation of fluid–particle interactions with the number of particles reaching 100. Comput Methods Appl Mech Eng 145:301–321

    Article  MATH  Google Scholar 

  79. 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 

  80. Tian FB, Xu YQ, Tang XY, Deng YL (2013) Study on a self-propelled fish swimming in viscous fluid by a finite element method. J Mech Med Biol 13:1340012

    Article  Google Scholar 

  81. Huang WX, Shin SJ, Sung HJ (2007) Simulation of flexible filaments in a uniform flow by the immersed boundary method. J Comput Phys 226:2206–2228

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

We are very grateful to Professor Joseph C. S. Lai and Dr. John Young at University of New South Wales Canberra for help in improving the paper. This work was conducted in part with grants under the National Computational Merit Allocation Scheme of the National Facility of the Australian National Computational Infrastructure, and was partly supported by the National Natural Science Foundation of China (No.81301291) and the Beijing Higher Education Young Elite Teacher Project (No.YETP1208).

Author information

Authors and Affiliations

  1. School of Engineering and Information Technology, University of New South Wales, Canberra, ACT,  2600, Australia

    Fang-Bao Tian

Authors
  1. Fang-Bao Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fang-Bao Tian.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tian, FB. FSI modeling with the DSD/SST method for the fluid and finite difference method for the structure. Comput Mech 54, 581–589 (2014). https://doi.org/10.1007/s00466-014-1007-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-014-1007-3

Keywords

Search

Navigation