A new implicit surface tension implementation for interfacial flows

A new implementation of surface tension effects in interfacial flow codes is proposed which is both fully implicit in space, that is the interface never has to be reconstructed, and also semi-implicit in time, with semi-implicit referring to the time integration of the surface tension forces. The main idea is to combine two previously separate techniques to yield a new expression for the capillary forces. The first is the continuum surface force (CSF) method, which is used to regularize the discontinuous surface tension force term. The regularization can be elegantly implemented with the use of distance functions, which makes the level set method a suitable choice for the interface-tracking algorithm. The second is to use a finite element discretization together with the Laplace-Beltrami operator, which enables simple reformulation of the surface tension term into its semi-implicit equivalent. The performance of the new method is benchmarked against standard explicit methods, where it is shown that the new method is significantly more robust for the chosen test problems when the time steps exceed the numerical capillary time step restriction. Some improvements are also found in the average number of nonlinear iterations and linear multigrid steps taken while solving the momentum equations. Copyright (c) 2005 John Wiley & Sons, Ltd.