> How do you define the stabilization when the viscosity/diffusivity has a
> discontinuity across the interface?  Make it a healthy jump of ten
> orders of magnitude.
I was talking about single phase one component flows.
One colleague of mine is working with multicomponent but the major issue there is still monotonicity.
VOF at high order is a big challenge too.
I know that there are dG schemes that works in case of very anisotropic diffusion coefficients (porous media applications), but I'm not an expert.

> > I think that the major difference is the convergence rates of iterative
> > solvers, with cG you need far less iterations. That's the reason why I use
> > cG for the pressure solvers in operator splitting algorithms for
> > incompressible flows.
> Okay, but then your discrete velocity field is only divergence-free up
> to discretization error instead of up to iterative solver tolerance.

Yes you are right. And in this context the skew-symmetric form is important to conserve energy.

Thanks for the paper link you posted.