I am solving two-dimensional compressible inviscid flows based on the Euler equations. To solve particular problems I wish to do, I have to define non-reflecting boundary conditions which is to prevent unphysical reflection from edges. However, most of NRBC are discussed in the context of acoustic equations. In fact, I don't know how to impose boundary conditions along edges in 2D.

Is there any good reference or test code? Before my defense, I have to figure it out . Please help me.

There is a classic reference by K. Thomson (maybe spelled Thompson) in Journal of Computational Physics (don't remember the date - roughly 15-20 years ago).

Check the paper of Poinsot and Lele,1992 , JCP they have a full detailed analysis of the NRBC for compressible Navier Stokes and Euler equations. Another thing to note is the context of acoustics is similar to what you are solving as majority of the problems in there also involves Euler equations to compute noise.Well along edges what you can is average the NRBC in both directions.

How do you apply bounday conition in the farfield if you are not sure it it's subsonic or supersonic inlet/outlet flows? I read something about the Riemann invariant but is unsure how to apply it. I am modelling a supersonic impinging jet and is unsure about the boundary that cuts across the wall jet along the plate.

Dear Jinwon,

One of the simplest absrobing BCs is to use the same flux scheme that you use in the interior on the farfield too. The only difference is that while the states for the flux at the interfaces are available for every interior face, on the boundary only one state is available from the cell that shares the face. The other state is to be supplied as the freestream. This BC works well both for subsonic and supersonic flows, even when the shocks/shear layers cross the boundary, wherein Riemann invariant fails. Of course, the classic references of Poinsot&Lele, Thompson and those of Giles will be of great help for understanding NRBCs.

Hope this helps.

Regards,

Ganesh