  A new model for the numerical simulation of a rigid body moving in a viscous
fluid flow using FEM is presented. One of the most interesting features of this
approach is the small computational effort required to solve the motion of the
rigid body, comparable to a pure fluid solver. The model is based on the idea
of extending the fluid velocity inside the rigid body and solving the flow
equations with a penalization term to enforce rigid motion inside the solid. In
order to get the velocity field in the fluid domain the Navier-Stokes equations
for an incompressible viscous flow are solved using a fractional-step procedure
combined with the two-step Taylor-Galerkin for the fractional linear momentum.
Once the velocity field in the fluid domain is computed, calculation of the
rigid motion is obtained by averaging translation and angular velocities over
the solid. One of the main challenges when dealing with the fluid-solid
interaction is the proper modelling of the interface which separates the solid
moving mass from the viscous fluid. In this work the combination of the level
set technique and the two-step Taylor-Galerkin algorithm for tracking the
fluid-solid interface is proposed. The good properties exhibited by the
two-step Taylor-Galerkin, minimizing oscillations and numerical diffusion, make
this method suitable to accurately advect the solid domain avoiding distortions
at its boundaries, and thus preserving the initial size and shape of the rigid
body. The proposed model has been validated against empirical solutions,
experimental data and numerical simulations found in the literature. In all
tested cases, the numerical results have shown to be accurate, proving the
potential of the proposed model as a valuable tool for the numerical analysis
of the fluid-solid interaction.
