  We develop a numerical method for simulating the dynamics of a droplet
immersed in a generic time-dependent velocity gradient field. This approach is
grounded on the hybrid coupling between the lattice Boltzmann (LB) method,
employed for the flow simulation, and the immersed boundary (IB) method,
utilized to couple the droplet with the surrounding fluid. We show how to
enrich the numerical scheme with a mesh regularization technique, allowing
droplets to sustain large deformations. The resulting methodology is adapted to
simulate the dynamics of droplets in homogeneous and isotropic turbulence, with
the characteristic size of the droplet being smaller than the characteristic
Kolmogorov scale of the outer turbulent flow. We report on statistical results
for droplet deformation and orientation, collected from an ensemble of
turbulent trajectories, as well as comparisons with theoretical models in the
limit of small deformation.
