subsonic and supersonic boundary conditions
 

Dear friends,
The following question is not yet quite clear for me:
In the literature we see many discussions for the boundary conditions for supersonic and subsonic cases. However, when we consider application of these conditions, for instance, an irregular tunnel with multiple outlets, inlet is subsonic and the shock wave exists somewhere inside, and some outlets are subsonic, some are supersonic. Even for the supersonic ones, the region close to the solid wall is still subsonic. The situation is so complex. How can I know if the boundaries are sup or subsonic? Is there any systematic way to make a judgement?
Thanks for your help.

Hi,

you can make the decision locally. If a boundary interface of a single cell is supersonic (based on the normal direction), you can prescribe all values from one side (either inside or outside, depending on if it is an inflow of outflow boundary -- this might also change over time).

If you know upfront if it is a supersonic boundary, you can also ignore the boundary layer and apply the supersonic condition for the whole boundary. This works well for external supersonic flow simulations -- for example the flow around a launch vehicle where you often truncate the domain at the base. I know that this is not strictly correct, but it works well nonetheless.

Otherwise my advice is simple: Try different approaches and find out what works best for you.

Cheers,
Oliver

To add to ogloth's explanation:

Take 2d case for simplicity. You have four eigenvalues

un, un, un-a, un+a

un = normal velocity at outlet cell face
a = sound speed

Assuming

un >= 0

then you have three outgoing characteristics. un-a may be positive or negative. If un-a is negative (normal flow is subsonic), then you need to specify one boundary condition which could be the outlet pressure (atmospheric pressure). If un-a is also positive then flow is supersonic and no boundary condition is required, everything is determined from the interior.