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 Johannes Schöön April 15, 1999 10:47

Boltzmann method for liquids?

Hi all!

Has anyone ever created a Boltzmann code for liquids?

(I reckon that a "billiard ball method" would fail at simulating cavitation, that's why I ask.)

Yours

Johannes Schoeoen

"master of research under the event horizon" (No matter how much work you throw in, nothing ever comes out.) dept. of Naval Architecture and Ocean Engineering Chalmers University of Technology, Gothenburg, Sweden

 John C. Chien April 15, 1999 12:32

Re: Boltzmann method for liquids?

I tried to read it a couple of times, still, I could not quite understand it. Then I realized that it is a beautiful painting. Over the light blue sky, there are white clouds. The ocean, the building, the boat and the north sea sky. Has anyone ever modelled the water like a smooth round billiard ball? Or is it easier to model the water droplet in the white clouds ? And " nothing ever comes out" is a beautiful painting by itself.

 Jackie Halliday April 15, 1999 23:10

Re: Boltzmann method for liquids?

The commercial code PowerFLOW is based on lattice gas/lattice Boltzmann techniques and it simulates both gases and liquids.

The website is www.exa.com

Jackie

 Johannes Schöön April 16, 1999 04:37

 Johannes Schöön April 16, 1999 04:50

Fluid rupture doesn't happen i a gas!

Apparently I have to be a little more specific.

The fluid 'inside' an ordinary Boltzmann method will respond to reduced pressures simply by gradually getting less and less dense. What I am looking for is a Boltzmann method with a 'working fluid' that acts like a true liquid, i.e., that will rupture once the pressure gets low enough.

Johannes Schoeoen

"master of research under the event horizon" (No matter how much work you throw in, nothing ever comes out.) dept. of Naval Architecture and Ocean Engineering Chalmers University of Technology, Gothenburg, Sweden

 Patrick Godon April 16, 1999 11:44

Re: Fluid rupture doesn't happen i a gas!

Hi there. It seems that what you are looking for is a CFD method that has the ability to represent a flow without any boundaries, except for the boundary of the liquid itself. I know two ways of doing that, the first is what you mentioned, namely a very low density region, but then you run into the problem of having to resolve both a high density and a low density region. The other method that I know that could do the job is the SPH method, short for Smooth Particle Hydrodynamics, method introduced in the late 80's. A good reference to it is: Joe Monaghan (from Monash University, Dept. of Math., in Australia), 1988, Comput.PHys.Comm. vol. 48, p.89. This method is being improved continually by Joe, and the best implementation can be found by looking at recent papers of Joe Monaghan in Journals like J.Fluid Mech., J. of Comput. Phys., etc... THe method is to represent the flow as interactive particles (of given mass). There is no need to treat the free boundaries, since there is a given number of particles (though some of them might be lost if they escape too far). The problem here is that regions with a small number of particles represent low density regions with a poor accuracy. Have a look at that and let us know if you are satisfied (hoping I understood you correctly). Cheers, PG.

 Johannes Schöön April 16, 1999 12:46

SPH is not a Boltzmann method!

From the subject line it may sound as if I will be splitting hairs here, but that is (hopefully) not the case.

SPH is but a method to discretize pde's, just like FDM and FEM. If you make the method Lagrangian, the 'node' points of the discretization will move around with the flow. However, these points are not 'physical' particles of the fluid, the interaction of which we try to simulate.

I had the benefit of working/modifying a Lagrangian FEM code shortly after reading one of the articles by Monaghan. That helped me (eventually) make this distinction.

Something with sticky(?) billiard balls is more like what I'm looking for.

Yours

Johannes Schöön

 John C. Chien April 16, 1999 14:34

Re: SPH is not a Boltzmann method!

You are looking for something like playing tennis with a tennis ball machine in a rainy day ? What has Boltzman done to the sticky billiard balls ? How many balls are you talking about at the same time, one or one billion?

 Patrick Godon April 16, 1999 14:52

The sticky particles method!

Hi there, I am back with a method that you might like, it is the sticky particles method (say of the order of tens of thousands particles or more depending onthe computer power). The method approximates the gas (or liquid if you prefer) with interactive particles. It conserves linear and angular momentum of colliding particles but it reduces and reverses the relative radial velocity of colliding particles (the radial direction is defined by the line joining two colliding particles). The 'stickiness' of the gas particles is adjusted by varying a parameter. This method is used in Astrophysics (together with SPH!!) and a main reference to it is: Thakar and Ryden, 1996, The Astrophysical Journal, volume no.461, page 55. You can get this in the library of Astrophysics at Chalmers. And when you go there you can give my best regards to Professor Marek Abramowicz (Astrophysics). Cheers, Dr. Patrick Godon.

 Adrin Gharakhani April 16, 1999 15:55

Re: Boltzmann method for liquids?

Johannes,

I would recommend that you contact Dr. Bruce Boghosian with your question. He might have worked on similar problems, and he is quite a helpful person (give my best regards to him please if you contact him). His website is http://buphy.bu.edu/~bruceb/ which will give you an idea of the type of work he does, and his email is there as well.

 Patrick Godon April 16, 1999 15:57

Why Boltzmann ..

Hi. I guess the Boltzmann appelation for a sticky particles method was probably introduced by Johannes since the statistics (in the classical limit) of identical but indistinguishable particles (here billiard balls, but ping-pong or tennis is ok too) falls into the class known as Maxwell-Boltzmann statistics. (in contrast to the Fermi-Dirac statistics for electrons, protons, neutrinos and the Einstein-Bose statistics for photons, pi mesons..). The Maxwell-Boltzmann statistics states that the number of gas particles of energy e desiganted by n(e) is given by: n(e)=exp(-alpha)*exp(-e/kT), where alpha is a very large parameter, T is the temperature and k is the Boltzmann constant (sometimes denoted as kB). It seems that a (relatively) small numbers of balls is enough to give good results (less than a hundred thousand). See my message on the sticky particle method. In fact it is equivalent to the SPH method in some sens. Cheers, Patrick.

 Ridwan April 19, 1999 09:23

Re: Boltzmann method for liquids?

Hello Johannes,

Contact Dr. Jos Derksen in our group. He developed a Lattice Boltzmann code for a stirred vessel using LES. his e-mail is: J.J.Derksen@klft.tn.tudelft.nl

good luck,

Ridwan.

 mecobio August 12, 2013 11:31

Quote:
 Originally Posted by Johannes Schöön ;2613 Hi all! Has anyone ever created a Boltzmann code for liquids? (I reckon that a "billiard ball method" would fail at simulating cavitation, that's why I ask.) Yours Johannes Schoeoen "master of research under the event horizon" (No matter how much work you throw in, nothing ever comes out.) dept. of Naval Architecture and Ocean Engineering Chalmers University of Technology, Gothenburg, Sweden
Well, the would be against the assumptions followed to obtain the Boltzmann equation. The gas is so dense that two particules trajectories are assumed to be independent of each others, before and even after collisions, that thus it simplies the manipulations of the equations until you get the Boltzmann equation (BE). The lattice Boltzmann (LB) equation is the discretization of the (BE). However, there existe a book on the subject on Lattice Boltzmann Methods for Shallow Water Flows:
http://www.springer.com/earth+scienc...-3-540-40746-1

That could be a good start for you.

Lycka till :)

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