A capillary free boundary problem governed by the Navier-Stokes equations

Abstract

In this paper an unsteady capillary free boundary in a viscous imcompressible fluid is studied from the numerical point of view. The linearized problem is formulated, and existence and uniqueness of a solution is proved. The linearized problem is discretized by a finite element method in space and a finite difference method in time. The numerical scheme is proved to be convergent and stable. The method is applied to the computation of free boundaries, eigenfrequencies, damping factors and vibration modes. The influence of the initial conditions, the boundary conditions, the contact angle, the Ohnesorge number and the Bond number is studied.