Can anyone explain what is the donor-acceptor flux approximation employed in Hirt's VOF algorithm for simulating free surface flow ? Thanks in advance

I think it is something like up-wind method. Try to get the original report from Los Alamos National Lab. There were several detailed reports published by Tony Hirt in 70's, including Fortran listing.

Hi Anthony,

If you go to the Los Alamos page

http://lib-www.lanl.gov/pubs/la-pubs.htm

then you can search the online catalog

Here is what I found:

Call No.:

LA-10612-MS Title:

NASA-VOF2D, a computer program for incompressible flows with free surfaces / Martin D.

Torrey ... [et al.]. Author:

Torrey, M. D. ; Los Alamos National Laboratory. ; Cloutman, Lawrence D. ; Mjolsness,

Raymond C. ; Hirt, C. W. Published:

Los Alamos, N.M. : Los Alamos National Laboratory ; Springfield, VA : available from NTIS,

1985. Description:

iv, 137 p. : ill. ; 28 cm. Tech. Rept. No.: LA-10612-MS

The report is scanned and can be downloaded from:

http://lib-www.lanl.gov/la-pubs/00306403.pdf

There is also a reference to an earlier paper and code: SOLA-VOF as given in report: LA-8355 1980 (I think this is the earlier work that John C is talking about).

If anyone has the source code for either of these I would appreciate getting it....typing is not my strong suit!!

good luck.................................Duane

As J.Chien mentioned in his response, the "donor-acceptor" technique is like upwinding, however there's one peculiarity about it. What the "donor-acceptor" technique does, it tries to estimate the fluxes of material (fluid) across a surface between two neighbor elements. These elements may both be full, both free surface or one full and the other free surface. Depending on the sign of the velocity between the elements, you assign a name of "donor" to the cell giving the fluid, and "acceptor" to the cell taking the fluid. The peculiar thing about the "donor-acceptor" technique is that the above distinction of the donor and acceptor cell is not enough to estimate material fluxes when at least one of the cells is a free surface cell. You can't just take upwind property and convect it downwind like an ordinary upwind would do. What more is needed, is the information about the direction of the local surface normal of the free surface. Depending on the orientation of the normal vector of the free surface with respect to the velocity vector between the elements, you need to calculate the material fluxes in a quite different way. Why it must be so complicated, just because one would like to avoid smearing of the free surface. The free surface should stay a sharp interface between two (or more) fluids. Despite a spectacular success of the "donor-acceptor" technique, it has some disadvantages. Probably the primary disadvantage is that, in its standard version, the corner coupling of the cells can be to weak for arbitrary free surface direction. Please note that the original "donor-acceptor" technique evolved since its origins. Besides the original reports (mentioned by the others) you may want to have a look at the paper by Lafaurie et al. (J.Comp.Phys.,113(1994)pp.134-147).

regards

DML

Thank you all! I have got some of Hirt's original reports from Los Alomos Laboratory via WWW. I deeply appreciate your kindness. But I got one more thing to ask. There seems to be many variants of original VOF algorithm. For instance, someone calculates over the whole domain including both fluid and air. This seems to try to avoid the difficulties in assigning the boundary conditions on the free surface. Is it really difficult to apply the boundary conditions on the free surface? or there is any thing i should take care while doing this? Thanks

Yes, you're right. Doing two-fluid calculations you avoid some problems with the free surfaces. Free surface is represented just by a jumps in thermophysical data (density, viscosity, etc.) and possibly some slip conditions. You may need to use a mixture-like approach for the free surface elements. There are two things to mention about running two-fluid calculations: 1. If you really need them, i.e. if you need velocities, pressures and temperature in both fluids, your equations (N-S, energy, continuity) may become more complex because of interfacial transport terms. 2. Calculations may be very expensive, success may be dependent on the problem studied. You may experience convergence problems when high property ratios (density, viscosity, etc.) between the fluids are involved. Your interface may smear out because of the mixture-like averaging. You can find some good old references on two-fluid (not always two-phase!) calculations using Spaldings GALA algorithm (Imperial College CFDU-Unit reports of seventies and eighties). From my experience, for problems where inertia forces are of primary importance one fluid calculations work better (if the physical problem does not exclude their usage). However, for one fluid calculations you must to impose stress boundary conditions. Success and accuracy of one-fluid calculations directly depends on actual implementation of the stress boundary conditions. Because there is no flux of momentum across a free surface, you have: SIGij Nj=0 where SIGij denotes ij-th element of the stress tensor in the fluid and Nj denotes appropriate component of the surface normal vector. If you take a product of the above expression with a normal and tangential surface vectors, you get two conditions which need to be imposed on a free surface. It is quite tricky to impose these tangential and normal stress conditions on the free surface. The degree of difficulty depends on your physical problem, its dimensionality (3D with strong free surface deformation is quite difficult), the mesh and the discretization you use. For some introductory presentation you may consult J.Comp.Phys.,8(1971)pp.434-448. Please remember that the cited paper deals with 2D simulation on a structured mesh. Extension to 3D and general meshes is possible but is more difficult than one would think.

regards DML

There has been a great deal of progress in volume tracking algorithms since Hirt's original VOF algorithm . If you are interested in more recent developments in this field please refer to:

Ryder, W.J. & Kothe, D.B., "Reconstructing Volume Tracking", J. Comp. Phys., 141, pp.112-152, 1998.

or check out this web site for recent publications by the folks at Los Alamos:

http://public.lanl.gov/mww/HomePage.html

Dear Duane I found an alternative way to have the source code without typing the whole code word by word. Actually, you can directly extract the desired code listing from the corresponding pdf file by acrobat reader's 'text selection tool' located in the tool bar, and then copy it to the text editor to do the necessary modification. Of course, you still have to check it carefully word by word because the whole document was scanned and some characters may not be recognized correctly.

Best Regards

The definition of the free surface location can be very time consuming, especially if one uses higher-order representation of the interface (in the original Hirt's method the representation is of the first order). Thus in VOF-methods volume-tracking is almost always explicit. With 'whole-domain'-approach one does not need to find the location of the interface for the solution, only as post-processing. Thus, one can trace the interface in explicit manner without strong complications. The special interface boundary conditions treatment is not necessary in this case, but this is not so important.

With best regards

''Thus, one can trace the interface in explicit manner without strong complications.''

in implicit, of course

Actually, the easiest way of describing all these methods is as a special convection differencing scheme used for the volume fraction equation, which preserves the sharpness of the interface. There's one implemented in STAR-CD for example, and you can find some information in the Issa-Ubbink ASME 1999 meeting; there's also a J. Comp Physics paper by the same authors.