I'm wondering what boundary condition is to be set at center line of my flow domain: 2D axisymmetric case, flow in pipe, air, subsonic, may contain shocks, inviscid, no-slip wall condition... can anyone advise?

Let me ask you a dumn question: What boundary are you talking about? Wouldn't any cell surface on that singular line have zero area (think 3D)? If so, would it matter what fluxes you assign on the "surface",... if flux times surface is zero, anyway?

right, but in 2D the line has certain length so it can be presumed certian flux will be passsing it.....

That's what it looks like, but do you see my point? Even though there is a length associated with that cell, the flux through the center line should be zero. This can be your "boundary condition". Remember that your 2D problem is just a simplified representation of the 3-dimensional one.

ahhhaaaaaa..... right you are.. just now I can see it. thanks a lot