I am trying to define the boundary conditions for the outflow boundary of a supersonic impinging jet. I tried using non-reflecting B.C. (sponge layer and characteristic approach) but there still appears to be reflections. if the outflow is supersonic would it be easier just to extrapolate from the interior? i am using Yee's(JCP 88:1990) upwind TVD schemes.

Shuo

The method of imposing boundary conditions on the characteristics usually works well even for supersonic flow. You might want doulbe check. It is true that if the flow is supersonic and the supersonic velocity is going "out" through the boundary then all your characteristics are actually out-going, and none is incoming. Usually one would set the incoming characteristics to zero to avoid any in-coming (relfected) wave. Make sure that you check the veolcity of the flow at that boundary to make sure it is supersonic everywhere and all the time, as if it is subsonic, then there will be an incoming characteristics that you will have to set to zero. In theory imposing the BC on the characteristics is enough to avoid the reflection of waves through a boundary, but it is better to set the in-coming characteristics to zero.