Skip to main content
SpringerLink
Log in

Simplified Fluid-Structure Interactions for Hemodynamics

  • Chapter
  • First Online:
Numerical Simulations of Coupled Problems in Engineering

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 33))

Abstract

Computing blood flows in a closed vascular system by isolating one section for simulation creates instabilities due to the time-periodic structure of the flow and possible non-physical back flow in the simplified geometry. We propose some solutions in the context of a simplified fluid structure interaction on a fixed geometry but with pressure dependent normal velocities at the compliant walls.The present analysis is based on the Surface Pressure model for the fluid-structure interactions.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Boffi D, Gastaldi L (2003) A fem for the immersed boundary method. Comput Struct 81:491–501

    Article  MathSciNet  Google Scholar 

  2. Deparis S, Fernandez MA, Formaggia L (2003) Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions. ESAIM:M2AN 37(4):601–616

    Google Scholar 

  3. Fernandez M (2013) Incremental displacement-correction schemes for incompressible fluid-structure interaction. Numer Math 123:21–65

    Article  MATH  MathSciNet  Google Scholar 

  4. 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 

  5. Formaggia L, Quarteroni A, Veneziani A (eds) (2009) Cardiovasuclar mathematics, MS and A series. Springer, Milano

    Google Scholar 

  6. Girault V (1988) Incompressible finite element methods for Navier-Stokes equations with nonstandard boundary conditions in \(R^3\). Math Comp 51(183):55–74

    Google Scholar 

  7. Gonzalez O (2000) Exact energy and momentum conserving algorithms for general models in nonlinear elasticity. Comput Methods Appl Mech Eng 190:1763–1783

    Article  MATH  Google Scholar 

  8. Gonzalez O, Simo JC (1996) On the stability of symplectic and energy-momentum algorithms for nonlinear Hamiltonian systems with symmetry. Comput Methods Appl Mech Eng 134:197–222

    Google Scholar 

  9. Hu Fang Q, Li XD, Lin DK (2008) Absorbing boundary conditions for nonlinear euler and navier-stokes equations based on the perfectly matched layer technique. J Comp Phys 227:4398–4424

    Article  MATH  MathSciNet  Google Scholar 

  10. Le Tallec P (2001) Fluid structure interaction with large structural displacements. Comput Methods Appl Mech Eng 190:3039–3067

    Article  MATH  Google Scholar 

  11. Nobile F, Vergana C (2008) An effective fluid-structure interaction formulation for vascular dynamics by generalized robin conditions. SIAM J Sci Comp 30(2):731–763

    Article  MATH  Google Scholar 

  12. Peskin C, McQueen D (1989) A three dimensional computational method for blood flow in the hearth-i. immersed elastic fibers in a viscous incompressible fluid. J Comput Phys 81:372–405

    Article  MATH  MathSciNet  Google Scholar 

  13. Peskin C (2002) The immersed boundary method. Acta Numerica 11:479–517

    Article  MATH  MathSciNet  Google Scholar 

  14. Pichon KG, Pironneau O (2014 ) Pressure boundary conditions for blood flows. Applied Math Conf in honnor of L. Tartar. Proc published in AIMS journal (to appear)

    Google Scholar 

  15. Pironneau O (1986) Conditions aux limites sur la pression pour les équations de Stokes et de Navier-Stokes. C R Acad Sci Paris Sér I Math 303(9):403–406

    Google Scholar 

  16. Pironneau O (1989) Finite element methods for fluids. Wiley, New York

    Google Scholar 

  17. Thiriet M (2011) Biomathematical and biomechanical modeling of the circulatory and ventilatory systems. Control of cell fate in the circulatory and ventilatory systems, vol 2. Springer, New York

    Google Scholar 

  18. Usabiaga F, Bell J, Buscalioni R, Donev A, Fai T, Griffith B, Peskin C (2012) Staggered schemes for fluctuating hydrodynamics. Multiscale Model Sim 10:1369–1408

    Article  MATH  Google Scholar 

  19. Vignon-Clementel I, Figueroa A, Jansen K, Taylor CA (2006) Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries. Comput Methods Appl Mech Eng 195:3776–3796

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire Jacques-Louis Lions, Sorbonne Universités, UPMC, Boite courrier 187, 75252, Paris Cedex 05, France

    Olivier Pironneau

Authors
  1. Olivier Pironneau
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Olivier Pironneau .

Editor information

Editors and Affiliations

  1. Centre Internacional de Mètodes Numerics en l'Enginyeria (CIMNE), Catalan Institution for Research and Advanced Studies (ICREA), and International Center for Numercial Methods in Engineering (CIMNE), Barcelona, Spain

    Sergio R. Idelsohn

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Pironneau, O. (2014). Simplified Fluid-Structure Interactions for Hemodynamics. In: Idelsohn, S. (eds) Numerical Simulations of Coupled Problems in Engineering. Computational Methods in Applied Sciences, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-319-06136-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-06136-8_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06135-1

  • Online ISBN: 978-3-319-06136-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation