# In which cases an interface tracking/capturing method needed along with Navier-Stokes solver for flow?

In my view, it is needed,

1. To save computational time.
2. To define accurate boundary conditions at interface where properties changes drastically.
3. To solver 2 phase problems as single phase only.
4. To capture breaking and joining of droplets/splashing.

Are there any other reasons which I am missing? Please guide. Thanks

• I find the question a bit too vague. Are you asking in which situations one uses free surfaces? Most problems that use the Navier-Stokes equations are of course formulated without free surfaces. Mar 16 '16 at 11:21
• In what since does #1 happen? In my experience, the physics drive the need to include free surfaces. If there's a flow with breaking waves or surface tension, you might need it to capture all the physical conditions you are trying to model. Mar 16 '16 at 17:31
• @BillBarth: See, I am trying to simulate flow in a box (e.g. mold box in castings). In that context, it will save the computation time on the cells which are not filled. And yes, it will help in capturing breaking and joining of streams. Thanks for adding the point. Mar 17 '16 at 9:40
• @WolfgangBangerth: Edited the question. Thanks. Mar 17 '16 at 9:45
• It seems you are confusing two concepts: a free surface occurs when there are several phases present with sharp(ish) interfaces free to move. An appropriate method needs to be used then, some track explicitly this free surface (e.g. ALE or immersed boundary methods), some don't (e.g. level set or phase field)
– Joce
Mar 17 '16 at 13:14

Free surfaces occur when there are several phases present with sharp(ish) interfaces free to move. Some methods allow to treat all the phases as a single mathematical problem (e.g. level set or phase field), while some others track explicitly this free surface (e.g. ALE or immersed boundary methods).

1. Can it save computational time? If you use a method as ALE method and solve only for one phase while simplifying the model of the other (e.g. assuming a perfect fluid with uniform pressure), the computational domain will be smaller but will usually have a more complex time-evolving geometry. This may not save time. On the other hand, if quantities like density are very different between the two phases, the condition number of the linear system associated will be much lower with ALE-like methods.

2. Two parts here:

a) Is it more precise? This will all depend on the meshing, a refined mesh in the location of strong gradients of physical properties can also be efficient, although the thickness of "interfaces" in implicit interface methods generally needs to be a few times the mesh size there.

b) What about the boundary conditions at the interface? Complex boundary conditions are usually easier to write at an explicitly tracked boundary, because you can usually discretise them directly rather than rewrite them in terms of quantities such as the level set function.

1. Your formulation is misleading. If you have two homogeneous phases and solve only for one using ALE-like methods, yes you will go from space-dependent parameters in an implicit interface method to homogemeous-parameter equqtion, but in general you'll think of it the other way: tracking the interface leads to two problems in two sub-domains.

2. Explicitly tracking the interface will require you to model the (de)coalescence events rather than just "capture" them. In general, if notheing is done, (de)coalescence events will give rise to mesh self-intersection. You need to prevent this by an explicit numerical modelling in explictly tracked interface methods, while for implicit interface methods this will happen seamlessly -- which doesn't mean that this will happen with the right physics.

• Nice explanation. To summarize: 1. It is not to save time at all. It is the need of physics (as pointed out by @Bill Barth) i.e. to model the reality of multi-phase flow interface. 2. Defining boundary conditions at interface one way or the other is just to bypass the requirement of finer mesh which increases computation time. 3. It is not like solving for one phase or for multi-phase, rather it is about formulating & solving specific equation(s) for specific phase. 4. Again, it is the need of physics, be it by tracking or capturing. Correct me if I am wrong. Thanks. Mar 18 '16 at 9:06
• 2: not really to "bypass the need of finer meshes", convergence in both type of approaches requires fine meshes and a posteriori error analysis will quite likely tell you that it needs to be finer in the interface area. For finite mesh size, there are possible biases like spurious tangential forces that may appear in the implicit interface method. 4: For both approaches, you need to work out the physics of (de)coalescence and check that you are reaching their asymptotic behaviour in your numerical simulation if you want to reproduce them accurately.
– Joce
Mar 21 '16 at 8:02