I am trying to use upwind TVD schemes to simulate an free underexpanded jet. What boundary conditions should I use and how long does it need to be with respect to the nozzle diameter. I am not simulating the flow within the nozzle itself hence the domians is just a rectangle.

Thanks Shuo

Dear Shuo,

You need to use NRBC conditions at the far boundary (such as those of Giles or Thomson&Lele), but an easier workable alternative is to employ a really far outer boundary (say 1000d, where d is nozzle diameter) and coarsen the grid as you approach the far boundary and employ Reimann invariant BC. (Reimann invariants are valid only under 1d isentropic assumption, this is violated here for sure, but the coarse grid close to the boundary adds enough diffusion to avoid any numerical instability; and the large length ensures that the shock diamond pattern typical of this problem is reasonably well resolved in the near field of the nozzle.

Regards,

Ganesh

For a free underpanded jet I ran a 2D simulation with a domain of D*3D, 100*300 grids. I used a = 0.085 and n = 6 for the sponge layer boundary parallel to the jet centerline. Initially you could see the shock diamonds within the jet but eventually the velocity became uniform. The region adjacent to the free jet was uniformly non-stationary. Can anyone please advise me on this?

Shuo