Free Boundary Flows on Unstructured Grids
Hi! The performance of the VOF, MAC schemes for the free boundary flows are well known and widely used. But all these approaches perform good on the cartesian grids (in 2 and 3 dimensions). I have tried to find any references on these methods for general (unstrucrured) grids but rather than Level Set method have found nothing. Could anybody give me a hint (positive or negative) whether it worth trying to implement VOF or MAC for the unstructured grids in three dimensions. Thanks a lot, George.

Re: Free Boundary Flows on Unstructured Grids
I have not gone throught the literatures, just some quick thoughts.
(i) If there is no other geometric complicity other than free boundary in the problem, there doesn't seems to be a need for unstructured grid, because VOF/MAC can take care of irregularity of the free boundary. (ii) One could consider using moving grid if the free boundary doens't break up. These are the reasons against unstructured grid VOF/MAC. But if there is a need for unstructured grid for other purpose other than free boundary, effort to implement VOF/MAC in unstructured grid would be justified. Regards, Jin Li 
Re: Free Boundary Flows on Unstructured Grids
Hi!
: These are the reasons against unstructured grid VOF/MAC. If you know, could you please list out these reasons. Sincerelly, George 
Re: Free Boundary Flows on Unstructured Grids
Hi George,
: If you know, could you please list out these reasons. Well, I just did in the previous poster. My argument is basically that if VOF/MAC can take care of irregular shape of the free sureface, then there is no need to use unstructured grid. It is my understanding that the main reason to use unstructured grid is to have bodyfitted grid. If VOF/MAC allows nonbodyfitted grid, there is no need to use unstructured grid if there is no other reasons. Best Regards, Jin Li 
Re: Free Boundary Flows on Unstructured Grids
OK, I understand your reasoning. But the problem is that VOF/MAC is suitable ONLY for the Cartesian grids (as far as I konow) or at least for grids that are toplogically equivalent to Cartesian ones, and with the Cartesian grids you can not get the boundary fitting: you always have steps that approximate the boundary. Suppose you have the complex geometry and your grid generator gives you the grids which consist of tetrahedrons + hexahedrons + prisms + ... etc. Such grids I undersatnd as unstructered. What to do in such a case? (ritorical question)

Re: Free Boundary Flows on Unstructured Grids
I am just trying to explore your original question "whether it worth trying to implement VOF or MAC for the unstructured grids in three dimensions", which I think is a good one. In principle I do not see why VOF/MAC cannot be implemented for unstructured grid. It's only that one has to work out all the possible intersection schemes for other elements such as tetrahedrons (it should be simpler than hexahedrons I suppose). However, the question remains is the motivation. Only to prove VOF/MAC works for unstructured grid? If VOF/MAC for Cartisianlike grid can model nonbodyfitted free surface, it should be able to model nonbodyfitted wall as well. Whether that is the best way of modeling walls is another issue. At least I can see one problem with VOF/MAC for Cartisianlike grid: if you have a very local structure to resolve, the locally dense Cartisiangrid will radiate out in all directions which makes Cartisiangrid very inefficient. That's an intrinsic problem for Cartisiangrid, and VOF/MAC will carry.

Re: Free Boundary Flows on Unstructured Grids
"and with the Cartesian grids you can not get the boundary fitting ..."
Actually, a pretty reasonable approximation to a boundaryfitted grid is available using FAVOR (Fractional Area Volume Obstacle Representation). FAVOR is described on the web site of Flow Science Inc, developer and publisher of Flow3D and one of the sponsors of this web site (www.flow3d.com). The name FAVOR is trade marked, but an explanation also appears in the following references: 1. Sicilian, J. M., and Hirt, C. W., An Efficient Computation Scheme for Tracking Contaminant Concentrations in Fluid Flows, 1984, J. Comp. Phys., v. 56, p. 428. 2. Martin D. Torrey, Lawrence D. Cloutman, Raymond C. Mjolsness, and C. W. Hirt, NASAVOF2D: A Computer Program for Incompressible Flows with Free Surfaces, Los Alamos National Laboratory Report LA 10612MS, 1985. As the title suggests, NASAVOF2D and its 3d successor NASAVOF3D, use both the VOF technique and FAVOR for flexibility in meshing and free surface tracking. Both Flow3D and the NASA codes grew out of the SOLA family of codes developed at Los Alamos in the 70's and 80's. 
Re: Free Boundary Flows on Unstructured Grids
OK, I've got the point. Roughly speaking the free surface problems can be partitioned into 2 groups:
(1) where the free surface defines the choice of the grid (e.g. the droplet falling into the liquid), and the external boundary (the walls) does not play the role; (2) where the walls and their approximation play important role (e.g. mold filling); For the first group the Cartesian grids is well inough, and I would not use the grids fitted to the interface in this case unless it brings in the new physics. For the second group the approximation of the walls and all wall effects can be nevertheless done using FAVOR but the framework of still Cartesian grids. But still the question remains: the advantages of the FAVOR is only due to the simplicity of the Cartesian grid generation compared with unstructured ones, or there are principal unavoidable problems in using VOF/MAC on such a grids (e.g. "bad" elements)? And what about partical methods? Sorry for two many questions. 
Re: Free Boundary Flows on Unstructured Grids
"But still the question remains: the advantages of the FAVOR is only due to the simplicity of the Cartesian grid generation compared with unstructured ones,"
The thread started out with unstructured vs Cartesian I think, leaving (structured) body fitted systems in the middle. The simplicity of grid generation of, actually, an orthogonal grid system (cylindrical and spherical as well as Cartesian) as opposed to either a body fitted or unstructured is an important consideration. But programming ease is also important. There's a lot of baggage in extra geometry and more complex differencing templates to be carried along in a body fitted algorithm. And it's even worse with the unstructured schemes. But you do get some flexibility in meshing for your trouble. "or there are principal unavoidable problems in using VOF/MAC on such a grids (e.g. "bad" elements)? And what about partical methods? Sorry for two many questions." Of course MAC stands for Marker and Cell, a particle method I think. I haven't tried to use VOF for a fixed boundary. I expect there'll be some other opinions posted soon. 
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