[Inquisitor101]

I have worked on this topic for a few years, so perhaps I ought to chime in. Hopefully this might clarify a few things on the matter for future readers.

Let's start off by addressing the elephant in the room: non-reflecting boundary conditions (NRBCs) are not an actual, physical conditions you see in real life (e.g. rigid walls). In fact, in real life, these correspond to "open" boundaries, implying they do not exist. You use them when you have truncated your domain and you're left with an "open" boundary. So, in its most basic and fundamental sense, a NRBC (ideally) must mimic an infinite domain -- as if that "open boundary" did not exist in your grid. In the discrete sense, however, this is defined by two things. A NRBC should:

• impose a desired boundary condition (BC).
• make sure no (numerical-)reflections exist.

The first point should be obvious: any BC must enforce some boundary state. Otherwise, the flow statistics will drift off. That is why you see terms like "partially non-reflective boundary conditions" exist, you need to gradually and weakly impose a target state to correct for the drift. At the same time, you need to decide how strong those "corrections" are, otherwise your non-reflectivity property will degrade. This, lies at the core of any NRBC methodology.

The second point is a little elusive to understand, perhaps. The notion of reflections here is a little tricky for someone who hasn't worked with these sort of BCs before. Let me clarify. Reflections here are not actual reflections, like when pressure waves reflect off a wall. Instead, these are numerical reflections which are reflecting off the open boundary. These are non-physical reflections, because this is an "open" boundary, hence in an open space, nothing should reflect off anything. The culprit behind their manifestation is solely an artifact of the numerical scheme and (subsonic) flow behavior taking place at the BC.

Mainly, you may think of NRBCs in two categories: a buffer zone one or a boundary-imposed one. Examples of the first are: sponge layer, perfectly matched layer, convective layers, etc.. Examples of the second are usually a characteristic-based implementation, e.g. NSCBC. Note, in each of those two categories, a plethora of sub-divisions exist. Just google any of those topics and you see a lot of papers discussing why their implementation is better on some problem.

That said, without going into the nitty gritty details, I need to point out something important here. In both cases (buffer zones or boundary-imposed), a target (or damping) state needs to be specified, otherwise your flow statistics will drift. This target state is usually the free-stream or far-field condition; In more complicated cases, it usually is obtained by averaging over a lower-fidelity simulation. That is why some folks consider a far-field condition to also be a part of NRBCs. It isn't non-reflective, per se, but it "tries" to address the same issue: handling of "open" boundaries. Usually, you can get away with a far-field BC as a NRBC if your problem and computational resources allow you to place that boundary far off from the physics your interested in. That way, grid-stretching and coarsening, along with the physical diffusion, will suppress most reflections emanating from your non-non-reflective boundary condition.