FEM and VOF / Level Set Methods

Christoph Lund

Intending to do some free-surface simulations, I would like to combine my FE-code (triangular Taylor-Hood elements, unstructured and fixed mesh, Galerkin residuals, unsteady incompressible flow) with some kind of VOF-method or Level-Set-method.

It would be nice if someone could give me some hints for the following problems:

Which kind of streamline-upwinding should be used for the Level-Set-function (the "concentration" function) to ensure a steep gradient and stable solution ?

Is a "re-initialization" of the Level-Set-function necessary ?

Using a VOF-method based on particle tracking, how can fluid properties (density, viscosity) be calculated on different quadrature points within the same partially (!) filled element ?