What is the cheapest free surface tracking algorithm?

By "cheapest", the computation time is the most important issue. This method can even be very inaccuracate. The volume loss problem, if not severe, can also be ignored. Strict stability condition (need larger timestep) can still be accepted.

In fact, I am search for a very simple and efficient to used in 3D computer graphics. Miscellaneous liquid effects (e.g.splash) can be artificially produced if they are not inclued in the computation domain. Speed is important because I hope this algorihm can be applied real-time and provide some user interfaction.

MAC (Marker-And-Cell) is simple, but it costs too much to convect the massless particles.

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.

(1). Please try to avoid asking several questions at the same time. (2). First, do the Internet search, or forum search. (3). Next, make sure that the question and answer will provide useful information. (4). Try to avoid the words such as "the best code", "the fatest method", ...etc. for obvious reason. (5). Present the problem you are working on clearly, such that readers can get a good picture first. (6). It is your responsibility to learn how to ask a question properly in the first place in a forum. It is not a computer game, shooting at a random target.

It was a very clear question. Thats is why I answered it. I guess if one can't answer it they will just be a critic.

sorry. a bit messy. It was a table. (Method) (CPU time)

Perhaps you should look at the vortex panel method as a solution strategy (especially if in 2D)

Adrin Gharakhani

Surface tracking is more than 2-dimensions needs a lot of code development, validation and verification. If you are talking about problems involving multiply connected domains (like splashing), I am not sure if there is anything simple out there.

Level set method is quite simple although there could be mass conservation problems (which you do not seem to concerned about). However, you would need a flow solver to go along with the level set method to predict the fluid dynamics.

If you already have a flow solver, try using an immersed boundary method (perhaps coupled with a level set method for interface tracking). Both immersed boundary and level set method are relatively easy to implemented when compared to other two-phase flow methods (which often require multi-level dynamic adaptation). Note, however that combining level set and immersed boundary methods is not trivial (though both method have been established for some time now). This has been proposed recently in a JCP paper but to my knowledge has never been done. Also, there are no apriori guarantees on accuracy.

Good luck.

Here are the details of teh JCP paper I mentioned in my previous posting.

The Immersed Interface Method for the Navier-Stokes Equations

with Singular Forces

pp. 822-842, Aug 10, 2001

Zhilin Li*, , Ming-Chih Lai

As I know, immersed boundary and level set method have benn implemented by sussman etc.

I. Aleinov, E.G. Puckett and M. Sussman, Formation of droplets in microscale jetting devices, to appear in Proceedings of FEDSM99, ASME conference, July 1999.

perhaps you can find it http://www.math.fsu.edu/~sussman/index.html