Direct Numerical Simulations of Oscillating Liquid Droplets: a Method to Extract Shape Characteristics

Oscillating droplets have been an object of various theoretical studies for more than a century and is one of the classic problems in fluid dynamics. A considerable number of theoretical models have been developed and many numerical simulations were conducted to investigate oscillating drops. However, the interplay between analytics and numerics is still not considered sufficiently and is capable of improvement. Thus, the main idea of this work is to extract data from numerical simulations to obtain an extensive comparison between numerics and the available analytical solutions. We present a method to extract surface coordinates of oscillating droplets from numerical simulations and perform a spectral decomposition into Legendre polynomials, in order to derive the different oscillation modes. Various simulations are performed with deviation of the initial droplet shape as well as varying viscosity. In addition, frequencies of the different modes are investigated and compared to analytical models. The method and the numerical results should serve as a basis to improve analytics and to motivate the development of more detailed oscillation models.