Very interesting post thomas. I intend to tackle most of what you wrote in FVUS/Wildkatze. I have few comments:

1. The diffusion term and gradient computations are big issue. I have in my mind extention of least square method that shall be much more accurate and method to estimate this diffusion term. I had previously implemented this method in starccm when i was developer there and tested for its accuracy against benchmark solution.
It will be implemented in FVUS project once the required framework for parallel is there. (since it requires extented stencil, providing proper support in parallel is not straight forward so it needs time that i don't have as of now).

2. Interface tracking would be much better done by iso-advector someoene implemented for openFOAM. In FVUS I have implemented THINC which is also very sharp so I do not think I need iso advection in FVUS. Point is this openFOAM has.

3. The most challenging part is linear solver. For FVUS it has something called auto-smoother, that performs much better for the cases which are very stiff. OpenFOAM needs this.

4. About the slip part, I worked on navier slip and it is quite difficult. However I have a patent that makes this slip implementation stable. Though patent is owned by my old employer, I have had in my mind another method to solve this problem. But for openFOAM this would be big challenge for someone who wants to work on it.

Hi everybody,
I have read your interesting work. I am also working on solutions of incompressible newtonian and viscoelastic mixtures.
Ata, have you released the solver? Your work would have been a great help.
Thanks in advance