I have a quesiton on how to define the difficulty for simulation of two phase flows with interface. If the flow is dominated by viscocity, it is simple If it is dominated by inertial, the interface shape changes a lot, it is not difficult the flow dominated by surface tension is the most difficult.

Then the problem is how to define the difficulty. Once there is a parameter named Ohnesorge number Oh= mu/sqrt(D rho sigma), but in there parameter, the diameter is beside the surface tension. As we know according to the Lapalace dp=sigma/r, small r means higher surface tension force.

Does anyone has a better idea?

Someone uses the level set method to distinguish the interface. Then the heviside function can be incorporated to determine density and viscosity across the interface.

rho=rho1*H+(1-H)*rho2 vis=vis1*H+(1-H)*vis2

where rho1 is density in phase 1 and rho2 in phase 2. H is a heaviside function ranging from 0 to 1.

Please refer to the immersed interface method, the level set method and so on.

You misunderstand my questions. My questions is to know how difficult the problem is, instead of how to represent the density.