We present an approach to simulate flows driven by surface tension
based on triangle meshes. Our method consists of two simulation layers:
the first layer is an Eulerian method for simulating surface tension
forces that is free from typical strict time step
constraints. The second simulation layer is a Lagrangian finite element
method that simulates sub-grid scale wave details on the fluid
surface. The surface wave simulation employs an unconditionally
stable, symplectic time integration method that allows for a high
propagation speed due to strong surface tension. Our approach can
naturally separate the grid- and sub-grid scales based on a volume-preserving
mean curvature flow. As our model for the sub-grid dynamics enforces a
local conservation of mass, it leads to realistic
pinch off and merging effects. In addition to this method for simulating
dynamic surface tension effects, we also present an efficient
non-oscillatory approximation for capturing damped surface tension behavior.
These approaches allow us to efficiently simulate
complex phenomena associated with strong surface tension, such as
Rayleigh-Plateau instabilities and crown splashes, in a short amount of time.