High order methods in commercial use?
I have a question for you guys working in industry / using / developing commercial codes:
In numerics research, there's a trend towards high order methods, high meaning significantly larger than 2, so maybe starting from 4 to about 16. For many (not all) flow situations, high order methods are usually superior in terms of efficiency and accuracy to first and second order schemes, but they come a price: They are usually more difficult to program, less stable (which I believe to be a good thing) and require more user knowledge.
I was wondering if there are any commercial codes out there that actually take advantage of higher order methods, or if you guys can observe a trend towards them, as in academia.... or might it just be that it will take a couple of years until they are adopted by the developers of commercial code?
Please give me your thoughts/comments on this matter!
Thanks and cheers!
OK, here is another spin on the question.
Outside of aeroacoustics, where are higher order methods useful? From the commercial side so many of the issues are about lack of knowledge of in depth best/worst practices, turbulence modeling, invalid and/or challenging boundary conditions (heat flow, moving surfaces, etc.), or inappropriate physics modeling for a given problem.
Hi Martin, thanks for your input!
I heared a talk today about rotary wing aerodynamicist using HO methods when investigating the effect of the rotor downwash on the tail rotor. With LO methods, the vortices just are lost on their way to the tail rotor. So wherever your flow features travel some distance and you need high fidelity, I guess HO methods could be useful.
Another application I saw today was about a supersonic gas injector, where they compared high order schemes to the results obtained with CFX (and HO beat the crap out of CFX ;) ). But I realize that the problem was simple in the way that there's no complex geometry involved.
Another application was to an airflow with moderate AOA, laminar separation, reattachment and transition, and a comparison with FV O2. The HO method were again superior.
Moving surfaces with HO shouldn't be any more trouble than with LO, right? I saw an impressive simulation of a bat in flight with HO methods....
So from my (limited) point of view, HO methods are maturing into a real alternative to LO methods, but I'm not doing practical engineering applications, so I realize that I might be missing some of the critical issues. Just what I saw in the last couple of days has shown me that people are doing HO methods successfully, from RANS to LES and DNS with complex, moving geometry and such. I have not seen any multiphysics stuff with HO, though, so there might be an issue with that.
OK, an example. Since I brought up helicopters in another thread, I'll use that. Sometimes, helicopter people will use RANS on the grid that is next to the blade and Euler on a cartesian grid for the off body flow. They also use higher order methods. But, from what I understand, they are not modeling viscosity in the far field in any way shape or form. Also, they use convergence of loading on the blade to determine the dt value. However, RANS equations are prone to be steady due to the high eddy viscosity. So how does one know if the dt value is appropriate or not? The non-linearities are extreme. A valid helicopter analysis, especially if there is a probability the vortex is interacting with something else, requires a lot of knowledge.
Will commercial codes go to higher order methods, probably since the expectation is there. Will it actually be useful, I'm skeptical.
P.S. I wrote my reply while you wrote yours. The fact that we both discuss rotor craft is coincidental. Yes, the HO method will maintain the vortex better for an Euler run. Add viscosity/turbulence into it, and I have no idea how the Euler run would compare to NS.
There was a nice discussion about this some time ago:
Article #8 of this thread describes best, what problems come from higher order methods.
Thanks a lot for pointing me to that post! I agree with the writer that shock capturing ( the first issue he raises with HO) is unsolved, and indeed HO methods sometimes have s buildin switch to revert to first order near shocks. So there is no advantage of picking HO over LO in these cases.
The writer is however wrong in the second case (LES). This actually is a field where HO methods outperform LO methods in terms of accuracy and efficiency - at least in a wide range of cases. The argument is that the dissipative and dispersive errors associated with a LO scheme are so much stronger than for HO scheme, they destroy your vortices and vortices are just the structures you want to resolve. You get a lot more quality per DOF with HO in such a case.
Another issue with HO methods is efficieny. People most of the time seem to equate HO with FVM HO for some reason. I agree that parallelizing a HO FVM will ruin your nerves and your parallel scaling, but other HO are perfectly scalable and outperform FV.
Btw, I just heard that Numeca are actually looking into HO methods. But if thats real interest with the intent to program it, who knows?
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