The main drawback of the level set method is its inability to rigorous conserve mass. This method can suffer from severe volume loss especially on relatively coarse grids commonly used in computer graphics. This is clearly visible when regions of liquid break away during splashing and then disappear because they are too small to be resolved by the level set.

In a SIGGRAPH paper, Foster suggested a hybrid system of level set method and "particles" to address this problem. Particles are introduced according in the high curvature regions (indicating splashing), where the particles are a better indicator of the free surface curve and are allowed to modify the dynmaic level set.

Are there any other special techniques to solve this problem? In computer graphics, we don't need very accurate algorithms, but that can capture significant visual effects (e.g. splashs).

Foster, N.; Fedkiw, R., Practical Animation of Liquids, in Proceddings of ACM SIGGRAPH 2001.

Recently my advisor and I did some simulations with jet pinch off and hitting the wall, and also hitting another liquid, most of them are relatively low Reynolds numbers, so you can hardly see the splash, but if we use high Reynolds numbers, you can surely see splashes. Visit my website and look at them.

They were used when my advisor gave a talk at Ford Car company.

http://www.ima.umn.edu/~junkim/ford.htm

What is the Reynolds number (and based on what). The jet flows in particular look very laminar - Re~O(1~10)?

Adrin Gharakhani

The Reynolds number were from 35 to 57 ranges, and simulations there weren't matched with experiment data. Those were just for testings, now I am doing comparisions with real experiment data with department of Aerospace

If you have more interests in that projects, visit our co project website.

http://www.aem.umn.edu/research/long...inch_off.shtml

And for the detailed parameters, look their papers. In their website.

http://www.aem.umn.edu/people/facult...longmire.shtml

Longmire, E.K., Norman, T.L., and Gefroh, D.L., "Dynamics of Pinch-off in Liquid/Liquid Jets with

Surface Tension," International Journal of Multiphase Flow, to appear 2001.

The Reynolds number is based on exit velocity, viscosity and density, diameter of jet.

How good is mass conservation in these simulations?

Traditional level set formulation has severe mass conservation problems. VOF methods, on the other hand, enforce strict mass conservation but are not as good in terms of capturing the evolution of the topology. I saw a recent paper which had a hybrid level set VOF in JCP. I have not had time to read it but is perhaps helpful here.

If you looking to model surface effects (surface tension, evaporation etc.), both level sets and VOF have problems. Then, I would suggest using diffuse-interface methods (also called phase-field methods). But they are unsuitable for graphics since the interfaces are smeared and no longer represented by a 2D surface.

Another method to capture fluid/gas interfaces is the MAC method (marcer and cell). Massless particles marc the liquid volume. The particles are moved by the flow field. The interface is kept within one cell so is the jump in the density. A disadvantage is its high computercost because 20 times more particles are needed then liquid cells and these particles need to be tracked during the time steps. You may search for terms like MAC, interface tracking and so on in your library. Some nice articles once were published in the web by Douglas B. Kothe and William J. Rider from Los Alamos National Laboratory. You may find these in your library.

A faster version of the traditional MAC algorithm was developed by Dehmel in his diploma thesis. The algorithm just need the particles in the cells adjacent to the surface and some cells below it called the particle depot. You find his work here:

http://www5.informatik.tu-muenchen.d...l/dehmel.ps.gz

Unfortunately it is written in German. But you may get the code from Prof. Zenger (look at http://www5.informatik.tu-muenchen.de). Just ask.