On the motion and collisions of rigid bodies in an ideal fluid

Article type: Research Article

Authors: Houot, Jean | Munnier, Alexandre^;

Affiliations: Insitut Elie Cartan UMR 7502, Université Henri Poincaré, Nancy 1, B.P. 239, F-54506 Vandoeuvre-lès-Nancy Cedex, France | E-mail: Jean-Gabriel.houot@iecn.u-nancy.fr | E-mail: Alexandre.munnier@iecn.u-nancy.fr

Note: [] Corresponding author.

Abstract: In this paper we study a coupled system of partial differential equations and ordinary differential equations. This system is a model for the 3d interactive free motion of rigid bodies immersed in an ideal fluid. Applying the least action principle of Lagrangian mechanics we prove that the degrees of freedom of the solids solve a system of second-order nonlinear ordinary differential equations. Under suitable smoothness assumptions on the fluid's domain boundary we prove the existence and C∞ regularity of the solids motion, up to a collision between two solids or between a solid with the boundary of the fluid's domain. The case of an infinite cylinder surrounded by a fluid in a half space cavity is tackled. By a careful asymptotic analysis of a Neumann boundary value problem (solved by the fluid's potential) when the distance between the cylinder and the wall goes to zero we prove that collisions with non zero relative velocity can occur.

Keywords: fluid–solid interaction, ideal fluid, Lagrangian mechanics, collisions, PDE–ODE coupled system

Journal: Asymptotic Analysis, vol. 56, no. 3-4, pp. 125-158, 2008