I have a question about the speed of algorithms used to tracking free surface.

VOF-like algorithm has to reconstruct the interface in the every time step, whileas the level set method not - construct once in the beginning, and evolve the interface hereafter.

Does this means that VOF algorithms are slower?

I have used level set methods quite a bit. For explicit marching they are quite fast. In my case there was a density jump across the interface and because of this, the convergence can sometimes slow down when an implicit scheme is used.

I have used a VOF type method once and in my opinion, VOF methods are slower (I am not sure how slow) compared to level set methods. You can not use VOF with implicit methods and so the comparison with level set methods does not arise in such a case. Also, if you are using a non-cartesian mesh, forget about VOF methods. These methods are usually demonstrated on cartesian meshes and I am not sure how the accuracy might suffer if non-cartesian meshes are used (in addition to the fact that reconstruction can be rather cumbersome and time-consuming). Be mindful however, that mass conservation is far better in VOF methods.

Kalyan

I wrote this a while ago, I hope the table comes out better. Personally I would be more worried about the speed of your Navier-Stokes solver more than the interface tracking routines.

Stretching and Tearing Interface Tracking Methods Rider and Kothe (find the paper on the web.)

CPU time (CRAY 64x64 grid) ------------------------------------- 1st.order.upwind......1.175.......... Level.Sets............1.406.......... SLIC..................1.787.......... Marker.Particles(1)...3.304.......... PPM...................3.351.......... Level.Sets.(Re-init)..5.995.......... PLIC..................6.887.......... Marker.Particles(4)..14.247.......... Marker.Particles(16).61.749.......... -------------------------------------

Of course this will vary with language used and programmers ability.

Dear JW Chiu

Forget speed problems and take into consideration two quite important issues to make your choise: mass conservation and interface spreading.

If you can use Level Methods (no topological changes in the interface nor interface multivalued function) I will recommned it over VOF methods.

I have performed a lot of calculations with VOF method and I can tell you that numerical difussion is present even if you use accurate interface convection-reconstruction schemes like PLIC (Piecewise Line Interface Contruction). Furthermore, the mass conservation is not a trivial problem. You should modulate the values of marker function in each cell after every time step.

I had studied atomization, so I had no choise and I had used VOF method, PLIC and surface tension forces for surfaces instabilities studies.

Level method has no aditional numerical diffusion and the mass conservation is guaranteed in each cell to move your interface level.

Make your choise based on accuracy; the time you will "save" with the actual machines is not representative in this comparisson (personal oppinion).

Regards

Kike

What do you mean by numerical diffusion in VOF methods. The interfaces are certainly not smeared. You construct (piece-wise planar) interface within each cell at every time step. The density and all other (phase dependent) material properties vary sharply across this interface.

Do you mean to say that the mass conservation is less of a problem with level set methods than VOF methods. I thought it was the other way around.

> Level method has no aditional numerical diffusion
: and the mass conservation is guaranteed in each cell
: to move your interface level.

If the problem has a flowfield with appreciable vorticity the level set method has demonstrated that in does not conserve mass. In the case where the underlying distance function is reinitialized, level set methods have the tendency to gain mass. If no reinitialization is done, the method tends to lose mass. Modern VOF methods such as PLIC do not suffer from these problems.

Another problem with the level set method is that the thickness is commonly chosen to be greater than one mesh cell wide.

Dear Kalyan

VOF methods are a 'family' of methods. From the original Hirt and Nichols scheme they have been developed until the last works of Li, Scardovelli and Zaleski (PLIC).

The numerical diffusion I was talking about is related (inherent) to the discretization of convection term into the scalar transport equation.

To avoid numerical diffusion is not enough to fix the interface as a line(plane) into the cell. The scheme of Hirt and Nichols consider the interface as this and you can get some interface smearing.

It is true PLIC has (formally zero) minimal numerical diffusion but it is also true you can have discontinuities of the interface at cell faces. The last work of Scardovelli (I don't think it is published yet) shows an enhanced PLIC method where it is elliminated. If you keep this discontinuities you can get an artifitially well deformed interface after some time steps. It is shown you can avoid this by inserting the surface tension effects (Brackbill or Zaleski models).

At the end, I had used (and I prefer) VOF method to track interface if I can not use surface particle tracking.

Regards

Kike

Kike,

I was thinking of interface reconstruction methods when I said VOF. Some of the recent papers in JCP (e.g. Rider, Kothe, Puckett) have overcome some of problems (like float-sam, distortions under rigid body motions) long associated with these methods. Collela, Bell (and their groups at LBNL) have also modeled 2-phase flows with volume based methods that conserve mass very well.

But the most useful version of volume based method I have come across was developed by Ubbink. I am not sure where it was published but you can download his thesis from the Prof. Gosman'g group website at imperial college. Since I do not work in 2-phase flows, I can not judge exactly how good this work is or what the shortcomings are. So, if you get a chance to read, I would like to hear your comments on this work.

Dear Zi-Wei Chiou

I am sorry, I think I was no clear in my comments and I didn't answer you question.

First, I had never used Level Methods, I know them as a part of interface tracking methods, but the case I have seen implemented in a general purpose code preserve the mass very well and has no numerical diffusion. Btw, the thickness you say was one cell length.

I repeat, I always work with VOF methods due tu the problems I study. Nevertheless, do you think that Level Methods are a proper choise if your flow field is like you describe ('with appreciable vorticity')?

I would say no, they are not. As you know vorticity is a well stablished source of non-linear instablities development near interfaces and I doubt that Level Method could be accurate under that conditions.

In that cases, the interface could becomes quite overtuned and I can imagine you should do beatifull things to make the method works. I will assume the results are like you say (no mass preserving) but I prefer to pointed that the choise you had made is not adequated.

You didn't gave us details about the flow type you want to simulate/describe in your first mail. So, tha comments you can have could be. (a)short, (b)general, and (c)maybe inappropriated (like mine). My answer to your questions is:

Yes, the VOF methods are always slower than Level Methods. It is mostly due to the reconstruction part of them. If you want a second order advection scheme you should use split techiques (alternate directions -Strang- or sequential fractional step methods -Yanenko-) to move the scalar marker. In that techniques you should reconstruct the interface, at least, two times each time step (in 2D domains) and it takes time and memory storage. If you use first order schemes you will save 'computational resources' (only one reconstruction each time step) but you will have large interface artificial deformations.

If I want your oppinion about the interface traking method I should use in one of my cases I should say: I want to simulate the dynamic of two cylindrical coaxial jets at Re=1000, We=250 and a density ratio of 1000. The region of interest is reduced to the near wake (3-5 jets' diameters) beyond the outlet and I use FVM code. After, I ask you (to all the colleagues of this forum) In your oppinion, what could be the better way to track the interface in such case?

Finally, I want to pointed that VOF tracking method has mass conservation as a consequence of the discrete representation of the conservation law by the advection algorithm, OK. Nevertheless, it do not guarantees you the mass conservation beyond your skills to handle convective fluxes by the advection algorithm and the numerical skills (errors estimation) you put in your code.

Regards

Kike