MULES advection scheme for compressible flows?
 

The MULES advection scheme is described in the report "Drop impact onto a liquid layer of finite thickness: dynamics of the cavity evolution", as well as in the report "A Coupled Pressure Based Solution Algorithm Based on the Volume-Of-Fluid Approach for Two or More Immiscible Fluids" where it is improved to work better for three or more phases.

In the first report, the flow is considered to be incompressible. I don't know about the second report because I can't access it right now (I'm getting a 404 message) but I guess that it also treats the flow as incompressible. But what about if you have a compressible flow? Can you modify the MULES scheme to cope with compressible flows as well? Is it described somewhere how you can do that and how the modified version of MULES for compressible flows would work? Thanks in advance.

Well, until I could read in both papers, no description of MULES is given far than naming it. MULES is based in Flux Corrected Transport (Zalezak's work) so that you could search about FCT in FVM for compressible flows and then do some changes in FOAM's code.

Regards.

Thanks, I found the reports Flux-corrected transport, I: SHASTA, a fluid transport algorithm that works by Jay P. Boris and David L. Book and Fully multidimensional flux-corrected transport algorithms for fluids by Steven T. Zalesak.

Is there any difference between the method used in Zalesak's paper and the method used in interFoam (which I guess is MULES)? Also, do you know if these methods conserves mass?

The principal conceptual difference between Zalesak's FCT and MULES we've found is the calculations of lambdas, their are the factors which control the amount of anti-diffusion used in the method. In Zalesak's work these are constant in each time-step while in MULES the calculation is iterative, but I don't know which is the loop finishing criterion. As is coded I think the method is less diffusive than FCT, but at the same time it could be more unstable. The other difference is the implementation, even though FCT is theoretically extensible to multi-dimension, that's not show in the paper. MULES is fully multidimensional, working by faces, the code is very tricky to understand. Some parts are not clear for me, I asked in this forum without answer, for example:

MULES::explicitSolve dimensions inconsistence

maybe it is proper to ask directly in FOAM Mantis.

There is a paper from Rudman where he shows the use of FCT in VOF problems, I think it could be treated as a "bridge" between Zalesak's work and the modern treatment found in FOAM MULES

Volume-Tracking Methods for Interfacial Flow Calculations

he compares it with SLIC and other reconstruction methods typically used in VOF, there aren't much differences. In fact in the last OpenFOAM workshop there was a lot of activity around VOF working with CICSAM (which had been dropped off from vanilla FOAM) and other schemes.

Respect to the conservativeness, MULES conserves volume, which in incompressible solvers implies mass conservation, but not in compressible ones. The other objective is to preserve boundedness. Maybe you can ask to Kent Wardle, he is working in interFoam related solver and dealing with the conservation:

multiphaseInterFoam

Hope this helps, and please post your findings to share the knowledge.

Regards