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Mathematical and Numerical Analysis of Some FSI Problems

  • Céline Grandmont
  • Mária Lukáčová-Medvid’ová
  • Šárka Nečasová
Chapter
Part of the Advances in Mathematical Fluid Mechanics book series (AMFM)

Abstract

In this chapter we deal with some specific existence and numerical results applied to a 2D/1D fluid–structure coupled model, for an incompressible fluid and a thin elastic structure. We will try to underline some of the mathematical and numerical difficulties that one may face when studying this kind of problems such as the geometrical nonlinearities or the added mass effect. In particular we will point out the link between the strategies of proof of weak or strong solutions and the possible algorithms to discretize these type of coupled problems.

Keywords

ALE method Elastic structure Existence of the weak solution Fluid–structure interaction Geometric conservation laws Hemodynamics Kinematic coupling algorithm Navier–Stokes equations Non-Newtonian shear-dependent fluids Operator splitting 

Notes

Acknowledgements

Céline Grandmont was supported by the grant ANR-08-JCJC-013-01 (M3RS project) of the French Research National Agency and by REO Project, Inria Paris Rocquencourt, Inria, France & LJLL, UPMC Univeristy, Paris, France, Mária Lukáčová-Medvid’ová was supported by the German Science Foundation under the grant LU 1470/2-2,3, and Šárka Nečasová was supported by the Grant Agency of the Czech Republic n. P 201/11/1304 and by RVO 67985840.

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Céline Grandmont
    • 1
  • Mária Lukáčová-Medvid’ová
    • 2
  • Šárka Nečasová
    • 3
  1. 1.INRIA Paris-RocquencourtParisFrance
  2. 2.Institut für MathematikJohannes Gutenberg Universität MainzMainzGermany
  3. 3.Institute of MathematicsAcademy of Sciences of the Czech RepublicPragueCzech Republic

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