Hi there,

I am working on a project for multi-phase flows of bubble simulations. The free boundary needs to be dealt with. The flow will be solved in a Eulerian frame (the NS solver is already there). I am struggling between using front capturing with the level-set function and front tracking with an independent Lagrangian mesh. I realized that each method has its own advantages and drawbacks. I'd be grateful if somebody out there could share with me his or her personal experiences on the accuracy, the efficiency, and of cause, the simplicity of these methods.

Regards,

Tony

Level set methods are simple and easy to use but when there are large density variations across the front, they tend to be problematic especially in terms of mass conservation.

I am pretty sure this is the reason why many of the solvers for multi-phase flows developed at Natl. Labs. use the VOF method. VOF methods have their own problems. For a long-time, they had the so-called "floatsam" problems which has now been fixed. These methods need front reconstruction (piece-wise planar or piece-wise parabolic) with each grid cell. On a 2-dimensional structured mesh, this is quite easy. For 3-dimensional meshes it takes a little more work and is perhaps not worth trying on a 3-D unstructured mesh. I have not seen it being used with unstructured meshes. Also this approach fits in well only with finite volume schemes. I have also not seen anyone trying to compute curvature dependent properties (like surface tension) in these methods.

If you want to use Lagrangian tracking using markers, the problem might become intractable after some time unless you regrid (which introduces some diffusion). I have read about this method but have never used it. I am sure there are a lot of fine implementational details that I do not know. I am guessing that it would take a long time to develop a code (longer than it would take you to develop level-set or VOF code) and debug it using this method. I suggest you take a look at papers by Profs. Tryggvason (U. of Michigan) and Daniel Joseph (U. of Minnesota) for a better overview on these methods. You can download some of Prof. Tryggvason's recent papers from his website (http://www-personal.engin.umich.edu:80/~gretar/).

Those methods(level set, VOF, Lagrangian tracking) are very popular in these days, but I'd like introduce another approach. It is diffuse-interface medel.

It couples Navier-Stokes equation and Cahn-Hilliard equation which incorporates surface tension terms.

Also, if you have interface breakup and merging, it cares them naturall, there is no artificial interface reconstruction.

One of my projects are simulating AntiBubble, which is three component fluid flows.

You can look at the website of Antibubble

http://www.jtan.com/antibubble/

Also my homepage

http://www.ima.umn.edu/~junkim/index.html

Kim

Hi Kalyan,

Thanks kindly. Actually, I've been reading both Prof. Tryggvasion's and Osher's papers. Their results are impressive.

My problem here is that the surface tension needs to be calculated as accurate as possible. The level-set is indeed simpler and easier to be extended to unstructured grid (I have to think so, since the NS solver I was asked to use is a FEM with tetrahedral mesh). However, the project I am working on will have a density ratio of 1:1000. And I have noted that the level set has some problems with mass conservation and front smearing.

The idea was to use VOF as makers and to convect an independent Lagrangian front. As you mentioned, re-initialization of the makers according to the moving front is needed, at least after a few time marching steps. On the other hand, the front itself needs to be reconstructed as well (smoothing and remeshing..., it would be a nightmare if the front becomes multi-connected). The communication between the front and the field needs also be well established. I can tell that there would be substantial searching and interpolation operations involved, and this would be not so easy in an unstructred grid.

My questions is: (1) I got to use a unstructured grid solver (not mine), (2) the density ratio is large, (3) surface tension is important, (4) I need to show some results within a few months.

Am I finished?

Regards,

Tony

Hi Junseok,

Thanks kindly for your response. The results seem convincing to me. However, what is exactly this method? Would you please provide me some detailed references?

And, what is the Cahn-Hilliard equation?

Thanks again.

Tony

A Diffuse-Interface Description of Fluid Systems D.M. Anderson, George Mason University G.B. McFadden, NIST

In classical models, an interface between two fluids is treated as infinitely thin, or sharp, and is endowed with properties such as surface tension. Diffuse-interface theories replace this sharp interface with continuous variations of an order parameter such as density in a way consistent with microscopic theories of the interface. Surface tension effects, for example, are incorporated into the model through a modified stress tensor in the classical Navier-Stokes equations.

from a website

http://math.gmu.edu/~dmanders/WEBDAN....html#diffuse1

And about the Cahn-Hilliard Equation http://www-sfb256.iam.uni-bonn.de/gr...LES/CH/ch.html

So, the basic idea is coupling Cahn-Hilliard equation and Navier-Stokes equation through advection and surface tension terms to model multi-phase fluid flow simulation.

D. M. Anderson, G. B. McFadden, and A. A. Wheeler

DIFFUSE-INTERFACE METHODS IN FLUID MECHANICS

Annu. Rev. Fluid Mech. 1998 30: 139-165. [Abstract] [Full Text]

Tony,

It seems to me that you are fairly well informed about the front capturing/tracking methods. Given that you just have a few months, the simplest approach might be your best option and at this point probably it is the level set method. I just hope that the people who are expecting the results from you realize how formidable the task is even with the simplest of the methods.

Junseok's suggestion about the diffuse-interface or the phase fluid approach also sounds good. It is more physics based than the level set method in that it involves an free energy minimization principle. There however are close parallels between the Hamilton-Jacobi (variational) formulation for the level set and this method. In the level set method, the interface propagation velocity has two components, the advective velocity (local fluid dynamic velocity) and a self-propagation velocity (e.g. flame speed in premixed flames, curvature dependent propagation of interfaces). It seems to me that that the right hand side of eq(21) in the Annual Review paper suggested by Junseok represents this self-propagation velocity (Junsoek, correct me if this is incorrect) and hence you can, in fact, easily replace level set equations with the Cahn-Hilliard equation should a mass error arise.

I'm assuming your dealing with air-water flows. If your surface tension is a very important force then you may want to use a particle tracking method (see Torres and Brackbill) also an preprint by Juric (search his homepage), also Marker Particles Popinet and Zaleski (search home page). VOF and Levelset techniques are still struggling with these issues. Vof methods more than LevelSet methods...

As for the 2 months issue... well if you have to do it from scratch in 3-d, sorry but good luck... You may want to settle with poor results from levelset and vof in this case and just use existing codes:

Sussman's Levelset code (homepage) Zaleski's VOF code (homepage)

Regarding your issue of dealing accurately with the surface tension, you may want to check into a new-ish method called the Level Contour Front Tracking method, which by formulation perfectly conserves the surface stresses in fully deformable interfaces. Check the newest issues of JCP and look for an article by Seung won Shin and Damir Juric of Georgia Tech.

The method is based on an adaptation of Damir Juric's version of Tryggvason's Front tracking. I am using this method to study internal bubbbly fows in heat pipes and nucleate boiling, and there are others in my group having great success with 3-dimensional film boiling.

[jdzlplq]

I have visited your homepage. The content of your homepage is very useful for me. However, the "code" term link on the homepage DON'T exist at the moment I visit. I looking forward to communicating with you.

Originally Posted by Junseok Kim
;16235

Those methods(level set, VOF, Lagrangian tracking) are very popular in these days, but I'd like introduce another approach. It is diffuse-interface medel.

It couples Navier-Stokes equation and Cahn-Hilliard equation which incorporates surface tension terms.

Also, if you have interface breakup and merging, it cares them naturall, there is no artificial interface reconstruction.

One of my projects are simulating AntiBubble, which is three component fluid flows.

You can look at the website of Antibubble

http://www.jtan.com/antibubble/

Also my homepage

http://www.ima.umn.edu/~junkim/index.html

Kim