  We studied numerically the dynamics of colliding rigid bodies in a Newtonian
fluid. The finite element method is used to solve the fluid-body interaction
and the fluid motion is described in the Arbitrary-Lagrangian-Eulerian
framework. To model the interactions between bodies, we consider a repulsive
collision-avoidance model, defined by R. Glowinski. The main emphasis in this
work is the generalization of this collision model to multiple rigid bodies of
arbitrary shape. Our model first uses a narrow-band fast marching method to
detect the set of colliding bodies. Then, collision forces and torques are
computed for these bodies via a general expression, which does not depend on
their shape. Numerical experiments examining the performance of the narrow-band
fast marching method and the parallel execution of the collision algorithm are
discussed. We validate our model with literature results and show various
applications of colliding bodies in two and three dimensions. In these
applications, the bodies move due to forces such as gravity, a fluid flow, or
their own actuation. Finally, we present a tool to create arbitrarily shaped
bodies in discretized fluid domains, enabling conforming body-fluid interface
and allowing to perform simulations of fluid-body interactions with collision
treatment in these realistic environments. All simulations are conducted with
the Feel++ open source library.
