Numerical simulation of a liquid drop freely oscillating

Free oscillations of a viscous liquid drop surrounded by a dynamically inactive ambient gas, in zero gravity, are investigated numerically using FIDAP (TM) package in the axisymmetrical case. The full Navier-Stokes equations with appropriate interfacial conditions are solved by using Galerkin/Finite element technique along with the spine method for the advection of the free boundary are used. The aim of this preliminary study is to demonstrate the ability of the package to accurately solve nonlinear free surface problems. Oscillations of viscous drops released from an initial static deformation of small to large-amplitude proportional to the second spherical harmonic, without initial internal circulation, are considered. Accuracy is attested by demonstrating that (i) the drop volume remains constant, (ii) dynamic response to small and moderate amplitudes agrees well with linear and weakly non-linear perturbation theories, (iii) large amplitude oscillations compare well with some numerical and experimental published results.