On a finite element formulation for incompressible Newtonian fluid flows on moving domains in the presence of surface tension

This work is concerned with the numerical modelling of incompressible Newtonian fluid flows on moving domains in the presence of surface tension. The solution procedure presented is based on the stabilized equal order mixed velocity-pressure finite element formulation of the incompressible Navier-Stokes equations, which is adapted to a moving domain by means of an arbitrary Lagrangian-Eulerian (ALE) technique. The accurate and very robust integration in time is achieved by employing the generalized-alpha method. The surface tension boundary condition is rephrased appropriately within the framework of linear finite elements. The solution procedure is verified by comparing numerical solutions with the corresponding analytical solutions and experimental data. The overall solution procedure proves to be accurate, robust and efficient. It allows the simulation of extensive deformation of the fluid domain without remeshing. Copyright (C) 2003 John Wiley Sons, Ltd.