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arXiv · 1212.1144

Fluid-structure interaction in the Lagrange-Poincare formalism: the Navier-Stokes and inviscid regimes

Henry O. Jacobs·Joris Vankerschaver
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Abstract

In this paper, we derive the equations of motion for an elastic body interacting with a perfect fluid via the framework of Lagrange-Poincare reduction. We model the combined fluid-structure system as a geodesic curve on the total space of a principal bundle on which a diffeomorphism group acts. After reduction by the diffeomorphism group we obtain the fluid-structure interactions where the fluid evolves by the inviscid fluid equations. Along the way, we describe various geometric structures appearing in fluid-structure interactions: principal connections, Lie groupoids, Lie algebroids, etc. We finish by introducing viscosity in our framework as an external force and adding the no-slip boundary condition. The result is a description of an elastic body immersed in a Navier-Stokes fluid as an externally forced Lagrange-Poincare equation. Expressing fluid-structure interactions with Lagrange-Poincare theory provides an alternative to the traditional description of the Navier-Stokes equations on an evolving domain.

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BibTeXRIS

Henry O. Jacobs, Joris Vankerschaver. 2012-12-05. Fluid-structure interaction in the Lagrange-Poincare formalism: the Navier-Stokes and inviscid regimes. https://doi.org/10.3934/jgm.2014.6.39

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