Dear all,

I recently work on the subject of a shock wave interacting with a very small sphere particle ( a few micrometers in diameter ), and the Reynolds number can be less than 100. The flow has to be considered as unsteady and compressible because of the existence of the moving shock wave.

Could anyone give any suggection or reference on such unsteady low-Reynolds compressible problems?

Thanks, Sun

Look at the Knudsen number. If it goes below 10 you'll need to look at rarified gasdynamics books.

The Knudsen number is less than 0.01, the definition of which might be the reverse of what you mentioned, and luckily the assumption of continuum is still valid.

I encountered a difficulity. If explicit schemes are used, the time step has to be propotional to the square of grid size for the low Reynolds problem. On the other hand, if an implicit scheme is used, it may loosen the restriction on the time step, but I am wondering whether it can capture a moving shock wave well?

An implicit scheme will not have problems in capturing the moving shock. That's more about grid resolution and the spatial scheme (TVD scheme are good at it). However, if you have to use small timesteps because your shock is moving with a speed in the order of the speed of sound and you want to see this movement in your results, implicit schemes are of no use. The overhead needed over explicit schemes is not usefull as you will be using small timesteps anyway. In my humble opinion its better to go for an explicit scheme if you stick to the moving shock problem.

Thank you.

My colleague had a bad experience that supports your opinion. He developed a complicated implicit code, hoping to enhance the efficiency for the computation of unsteady viscous flows with moving shock waves, but finally he said he gained nothing compared with a simple two-step explicit code. It seems an implicit scheme does not help a lot for such a problem.

Mingyu Sun

Good to hear I'm right on this one. Keep me posted on the results. I'm curious on what you're doing.

I work mainly on unsteady aerodynamics with shock waves. Shock/sphere interaction is a simple model of shock interaction with dusty gases, or the motion of tracer particles in supersonic wind tunnel flows with shock wave, etc. Oh, I am a little bit out of date, always write programs by myself. I have quite long experience in programming and validating compressible inviscid flows, and convection-dominated viscous flows, but have little knowledge on such low Reynolds flows. I hope to hear opinions from experts on this field before writing an implicit code or trying to find a new way to solve the problem.