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Robin-Neumann Schemes for Incompressible Fluid-Structure Interaction

  • Miguel A. Fernández
  • Mikel Landajuela
  • Jimmy Mullaert
  • Marina VidrascuEmail author
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)

Abstract

Mathematical problems involving the coupling of an incompressible viscous flow with an elastic structure appear in a large variety of engineering fields (see, e.g., [14, 17, 19–21]). This problem is considered here within a heterogenous domain decomposition framework, with the aim of using independent well-suited solvers for the fluid and the solid. One of the main difficulties that have to be faced under this approach is that the coupling can be very stiff. In particular, traditional Dirichlet-Neumann explicit coupling methods, which solve for the fluid (Dirichlet) and for the solid (Neumann) only once per time-step, are unconditionally unstable whenever the amount of added-mass effect in the system is large (see, e.g., [5, 12]). Typically this happens when the fluid and solid densities are close and the fluid domain is slender, as in hemodynamical applications. This explains, in part, the tremendous amount of work devoted over the last decade to the development of alternative coupling paradigms (see, e.g., [7] for a review).

Keywords

Implicit Scheme Incompressible Viscous Flow Fundamental Ingredient Explicit Coupling Kinematic Perturbation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work was supported by the French National Research Agency (ANR) through the EXIFSI project (ANR-12-JS01-0004)

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Miguel A. Fernández
    • 1
    • 2
  • Mikel Landajuela
    • 1
    • 2
  • Jimmy Mullaert
    • 1
    • 2
  • Marina Vidrascu
    • 1
    • 2
    Email author
  1. 1.Inria Paris-RocquencourtLe Chesnay CedexFrance
  2. 2.Sorbonne Universités, UPMC University Paris 6, Laboratoire Jacques-Louis LionsParis Cedex 05France

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