# Speed of VOF v.s. Level Set Method

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 October 1, 2001, 12:25 Speed of VOF v.s. Level Set Method #1 Zi-Wei Chiou Guest   Posts: n/a 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?

 October 1, 2001, 14:28 Re: Speed of VOF v.s. Level Set Method #2 kalyan Guest   Posts: n/a 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

 October 1, 2001, 15:51 Re: Speed of VOF v.s. Level Set Method #3 Mr. Question Guest   Posts: n/a 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.

 October 4, 2001, 05:34 Re: Speed of VOF v.s. Level Set Method #4 Kike Guest   Posts: n/a 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

 October 4, 2001, 12:29 Re: Speed of VOF v.s. Level Set Method #5 kalyan Guest   Posts: n/a 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.

 October 4, 2001, 13:53 Re: Speed of VOF v.s. Level Set Method #6 Zi-Wei Chiou Guest   Posts: n/a > 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.

 October 4, 2001, 14:20 Re: Speed of VOF v.s. Level Set Method #7 Kike Guest   Posts: n/a 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

 October 4, 2001, 15:17 Re: Speed of VOF v.s. Level Set Method #8 kalyan Guest   Posts: n/a 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.