In the present paper freely sedimenting n-butanol droplets in water are simulated by means of computational fluid dynamics. The finite-element and the extended finite-element methods were implemented and evaluated. The level-set function is used for capturing the interface movement. The three-dimensional nonstationary simulations included the stages of droplet acceleration, deformation, and stability in terms of shape and velocity. The influence of the grid resolution, the computational domain walls, and the droplet initial velocity was investigated and quantified. The droplet diameters that were studied spanned the region of spherical, deformed, and oscillating droplets. The simulation results were compared to experiments and empirical models in terms of droplet shape, oscillation behavior and terminal velocity, showing good agreement. The extended finite-element method was found to provide simulation results in better accordance to the experiments and empirical models than the conventional finite-element method. (C) 2009 Elsevier Ltd. All rights reserved.