I am currently working on an optimization project for transonic airfoils. The idea behind it is to combine a slow-but-accurate ("fine") model with a fast-but-inaccurate ("coarse") model.

Currently I am using a multigrid Euler solver with different grid sizes and settings for both the fine and the coarse model. It would be interesting to see whether the optimization scheme keeps working when the models used are more different.

The natural way to look for coarse models is to look at the kind of codes used before Euler codes. As far as I can tell, these used to be either Transonic Small Perturbation methods or Full Potential codes.

I have found a public domain TSP code, named Transfoil, but I can't find a Full Potential code. Does anyone have a suggestion for this? My suspicion is that Full Potential codes disappeared because they weren't appreciably faster than the newer Euler codes, but I can't find explicit confirmation for this. Can anyone confirm this?

Thanks in advance!

ps. of course other suggestions for a fast-but-inaccurate model are welcome. In the future I might become interested in more-accurate-but-slower-than-Euler models. Euler with boundary layer corrections seems the natural step, but these appear a bit too messy to be used in an automated optimization scheme. Anyone with experience?

The potential flow equations can be solved relatively rapidly (much faster than the full Euler equations) using Boundary Element Methods. A search for articles on the "Panel Method" should give you some references. These Methods can also be applied to compressible (subsonic) steady flows.

The trouble is that standard potential methods cannot handle flows with both sub- and supersonic regions. Basically, they can't treat shocks.

For airfoil optimization those shocks form exactly the interesting part of the solution, since they produce significant drag.

Apparently, there were some codes in the 80s that could handle shocks, these are the "full potential" codes I am interested in.

But thanks for the reply!

The transonic small disturbance methods can be used to model shocks and to optimise airfoils. The first useful Transonic Euler method (Yoshihara) actually came before the first TSD method (the MC scheme). I've not got much experience with full potential methods so I don't know how useful they are for this type of problem.

The TSD scheme has been used for optimization problems before although it may be a tad inaccurate for what you want to do. There's plenty of info in the literature for TSD optimization (unfortunately I'm away from the office at the mo so I can't look any up for you).

Have fun, B

"The trouble is that standard potential methods cannot handle flows with both sub- and supersonic regions. Basically, they can't treat shocks."

That's because the flow is not strictly speaking potential if there is a shock - the Kelvin/Helmhotlz therorems are violated at a shock. The best you can hope for is that the region where the flow is not irrotational is very thin and so can be modelled as a surface of discontinuity separating two regions of irrotational flow. In practice you'd be better off solving the full Euler equations with a shock capuring algoithm (which will also guarantee you pick up the correct physical solution).