Variational discretizations for the dynamics of fluid-conveying flexible tubes

François Gay-Balmaz (1) , Vakhtang Putkaradze

1 LMD - Laboratoire de Météorologie Dynamique (UMR 8539)

We derive a variational approach for discretizing fluid-structure interactions, with a particular focus on the dynamics of fluid-conveying elastic tubes. Our method is based on a discretization of the fluid's back-to-labels map and a Lie group discretization of the tube's variables, coupled with an appropriately formulated discrete version of the fluid conservation law. This approach allows the development of geometric numerical schemes for the dynamics of fluid-conveying collapsible tubes, which preserve several intrinsic geometric properties of the continuous system, such as symmetries and symplecticity. In addition, our approach can also be used to derive simplified, but geometrically consistent, low-component models for further analytical and numerical analysis of the system.

xml:lang="fr"

Mots clés: Variational integrators; Fluid-structure interaction; Fluid-conveying tubes

Domaines: Planète et Univers [physics]

François Gay-Balmaz, Vakhtang Putkaradze. Variational discretizations for the dynamics of fluid-conveying flexible tubes. Comptes Rendus. Mécanique, 2016, 344, pp.769-775. ⟨10.1016/j.crme.2016.08.004⟩. ⟨insu-03727099⟩