A new implementation of surface tension effects 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 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.