During a short discussion with a collegue of mine, the following (maybe stupid) question arises: what's the meaning of simulating Newtonian flows at Re<1000 and Mach>0.1 for an ideal gas? From the points of view of engeneers, what kind of flows in reality satisfy these parameters? Every consideration is well accepted.

Mach>0.1 is a little confusing, why not say Mach>0 ? You are basically wondering about low-Re ideal gas flow, is that right? Is your question with respect to the validity of the "ideal gas" model, or the "Newtonian stress" model, or both?

No No, sorry I had to give a better explanation. I am just thinking in "dimensional" way. Consider a physical problem (any!), fix the gas (ideal) and a reasonable length scale; derive Re and M and try to see if the non dimensional parameters can be like I mentioned ( M>0.1 and Re<1000) I haven't found one example!

Rarefied gas flows probably? Something travelling in the atmosphere high and fast enough. But in this case you also have to worry if the gas still can be treated as continuum. A crude estimation: Kn=1.21M/Re. Your values give Kn about 0.0001 so it's pretty continuous.

Maybe a heavy gas at low temperatures and very low pressures and a scale of 0.1 m (teh smaller the better) Say Krpton at 173 K and few Pascals of pressure which would give you a speed of sound of 163 m/s and a viscosity of ~1.5E-5. I think the numbers add up Of course in nature I can only imagine weird planets with very low atmosphere and some internal heating, maybe Mars, or some Jupiter moons? The continumm number would be as well another thing to check, but playng with the appropiate pressure you can keep a very thin atmosphere but just in the borders of continuum. If the temeprature drops too much (below ~100 K) this gases boil so the numbers will not be valid.