The purpose of this work is to investigate the falling dynamics of thin disks immersed in a viscous fluid using direct numerical simulations, coupling the Navier-Stokes equations with the equations of motion of a rigid body. Extensive analysis has been performed for studying the influence of geometric and physical parameters, such as the aspect ratio, the ratio of external and internal diameters of the discs, and the density ratio between solid and fluid. This led to the mapping of a phase diagram whose parameters are the Reynolds number and the dimensionless moment of inertia, identifying various types of falling styles according with [1], [2]. The study also explores the stabilizing effect of a hole in the geometry similarly to [3] and investigates the effect of the Strouhal number in the transition from one mode to another. The process consists in, firstly, solving the solid dynamics in absence of external fluid forces, secondly, solving the fluid dynamics to determine velocity and pressure fields. Through these, we computeed the external forces acting on the body using potential flow approximation and then we solved solid dynamics adding also these force terms. We obtained the updated body velocities that represent boundary conditions for the fluid problem at the new time step. The obtained results show that numerical simulations allow characterizing the behavior of coupled systems both quantitatively, through the Strouhal number, Euler angles, and velocities, and qualitatively, via trajectory and the visualization of the velocity and pressure fields.