Hi, I am looking for good references about velocity boundary conditions in the MAC (Matker - and - Cell) type solvers (staggered grids, uvp, etc.).

The problem I mean is that I suppose that simply trating free surface by satisfating the incompressibility condition (zero the divergence on the free surface) is actually not enough if it is staightforward applied like it was presented in Harlow, Welch works from Los Alamos University.

Does anybody know good and new reference about that? Maybe somebody has discovered it so far?

Best Regards, Maciej Matyka don't click here

This is a really outdated method. In fact, the Simplified MAC method (SMAC) was released by the Los Alamos group within the same year. The SMAC method reduced the programming and computational work by about 50% from MAC while getting identical answers.

Frank Harlow retired from LANL last fall after 50 years! in CFD (and other) physics.

You might want to look at SOLA-VOF - have your library check J. of Comp. Physics for Harlow, Hirt, etc. SOLA-VOF uses many of the same ideas developed in MAC/SMAC but has a modern free surface treatment and improved differencing and iterative techniques.

The themes developed in SOLA-VOF have been expanded in the commercial CFD code Flow-3D.

Do you think there is no place for improved MAC solver? I am working on 2d solver which simply get the way of fluid tracking (markers) from MAC method and uses SIMPLE algorithm (Patankar) for solutiuon to NS equations.

The reason why I want to use markers in whole fluid, not only on the surface is that it simply gives me possibility to track the fluids movements inside of the flow, what you loose when you track the surface only.

I will look into SOLA-VOF code since the MAC surface conditions described in Harlow and Welch papers from LANL are little confusing - involves nonsymmetries etc. Will try to fix that.

The next reason for using the MAC markers method is that it is straightforward to implement and I think and claim that it is one of the most intuitive method for solution to NS free surface problems ever developed.

Thank you for pointing me that method, btw. could you give me more references to that method?

Best Regards, Maciej Matyka <A HREF="http://panoramix.ift.uni.wroc.pl/~maq/eng/">http://panoramix.ift.uni.wroc.pl/~maq/eng/</a>

Lots of questions! : )

First, the SMAC is essentially identical to MAC. It's just that the calculation is rearranged, resulting in a much easier equation for the pressure correction. The method was described briefly in a JCP article within a year of the first paper on MAC. There's also a detailed LASL (now LANL) report on both MAC and SMAC. The two handle the free surface - or surface interface identically, using massless marker particles.

These fell out of favor because a lot of particles were required to track the surface/interface accurately, and the memory and CPU costs to do this taxed the best computers that LASL had available. And those were the fastest in the world at the time.

C. W. Hirt proposed simple alternatives to the marker particle technique in at least one JCP article in the late 60's and early 70's. They only worked when the surface shape was single-valued - that is, it wouldn't work with a breaking wave or such.

In the late 70's, Hirt published a code called SOLA-SURF, which added surface tension to the free surface treatment. Again, an article in JCP and a LANL report resulted as well as application articles in other journals.

The surface tension stuff was carried forward into SOLA-VOF, JCP article (and others) and a LANL report.

All of these methods/codes retained the marker particle coding. In all except MAC and SMAC it was used stictly to track the fluid as you wish to do. Of course with more memory, faster computers, and improved algorithms to handle the particle motion, the markers don't extract the same cost from the user as they did in the beginning.

"Do you think there is no place for improved MAC solver?" Not to mark surfaces. But, used with VOF, it is a great visualization method. And, since you aren't trying to keep up with the surface using the markers, you can use relatively few to generate streak lines.

"The reason why I want to use markers in whole fluid, not only on the surface is that it simply gives me possibility to track the fluids movements inside of the flow, what you loose when you track the surface only." Right on!

"could you give me more references to that method?" Beyond the Journal of Computation Physics (JCP) articles, I don't know. I understand that LANL and other US Government libraries have limited distribution of reports since 9/11. But there must be lots of copies of those reports (and the codes) out there - after all we're talking 1960's through the early 90's.

Good luck.

I like the MAC method because the free surface thickness is one cell only. In all other methods like VOF the surface is smeared over 2 to 3 cells.

In traditional MAC the complete fluid region had to be marked with particles which was of course very expensive. There was a method developed by Prof. Zenger from the Technical University of Munich some years ago in which the particles were only neccessary in the cells including the free surface and one or two cell layers below it. The following link might give you a starting point to dig out more literature: http://www-lit.ma.tum.de/veroeff/htm...002.76003.html

Thank you for taking a voice in that discussion. Actually you helped me to deicide if I should still develop the MAC method.

Maciek

"First, the SMAC is essentially identical to MAC. It's just that the calculation is rearranged, resulting in a much easier equation for the pressure correction."

I am trying to connect the Free Surface tracking from the MAC Method with SIMPLE (Patankar) procedure for solution to NS - it means I will have even more clear solution than SMAC gives. Am I wrong here?

"These fell out of favor because a lot of particles were required to track the surface/interface accurately, and the memory and CPU costs to do this taxed the best computers that LASL had available. And those were the fastest in the world at the time."

Do you know papers by Sean McKee? He is developming MAC Method still (GENSMAC code) and I fill he is going into right way - MAC is computationaly cost, but gives something - a quite accurate surface and fluid flow tracking and - most important - is quite easy to implement and understand (I mean the particle part, not pressure equation which for original MAC is quite messy).

Best, Maciek