i run the code of compressible N-S equations, and compare the results with incompressible ones because of low Mach number, about 0.2. is it right? Re=3900 ,cylinder.

I have never done such comparisons, but you should go lower with your Mach number. What "they" say is that low Mach starts at 0.1. You have to be careful though, when the Mach number becomes too small, most compressible codes produce false result, especially false pressure distributions.

Actually flow can be considered essentially incompressible up to a Mach number of ~0.3. You can show this very simply (and get a bound on your error) by doing a Taylor series expansion of the density ratio as a function of Mach number. You should be fine.

M=0.1 is generally used for incompressible flows, see for example

Morgan, P. E. and M. R. Visbal. 2001. Simulation of Unsteady Three-dimensional Separation on a Pitching Wing. AIAA Paper 2001-2709

It works well, is below the M=0.3 limit, but still high enough to avoid numerical errors. M=0.01 is probably to low though.

Question is: What type of comparison are you trying to make at Re = 3900?

-- Jarmo

I will compare the velocity counter and Pressure, but density field is very different because of fluction! i want to validat my code by computing the cylinder flow.

If you run it at M=0.1 the fluctuation should be much smaller, if it still persists, you may have some other problems (is your farfield "far enough", are you comparing with experiments or computations, and so on)

You may also want to compute some Re ~ 100 as it is easier to validate.