A new implementation of surface tension eects in interfacial flow
codes is proposed which is both fully implicit in space and semi-implicit
in time. The main idea is to combine two previously separate techniques
to yield a new expression for the capillary forces. The first is the contin-
uum surface force (CSF) method, which is used to regularize the discon-
tinuous 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.
KEY WORDS: multi-phase flow, implicit surface tension; finite elements;
level set method