I'm an electrical engineer myself and usually try to suppress the engineering topics because it ends up being more involved than people usually want to get (nothing wrong with that either)...so I enjoy an opportunity to talk engineering speak
Do you tune the simulation with equalization to represent the room's response?
Not sure what you're referring to here???
Also so can you explain the difference between boundary gain and room gain? Thanks.
Here's how I understand it:
Measure the subwoofer in the middle of a field - this will be half-space. Now measure the subwoofer sitting beside a really big building (basically a big wall in the middle of a field). This gets you a 1/4 space measurement and ideally you'll see +3dB at every frequency relative to the 1/2 space measurement. Then measure with a big corner out in the middle of a field....so a 1/8 space measurement. You'll ideally see +3dB at every frequency compared to the 1/4 space or +6dB from the 1/2 space.
What's happening is the energy that would normally be travelling rearward is reflecting off the wall and being redirected forward. Therefore, the intensity (amount of energy per area) increases in front of the speaker. The intensity at a single point in space is what is being shown in a normal frequency response plot. If you integrate the intensity over all space, then you end up with the power response (the total energy being delivered by the speaker at each frequency).
The +3dB from halving the space the driver is firing into is true when you assume that the speaker has an omnidirectional polar pattern and that the reflections take zero time to occur. So the only time this is true is for a point source located on the vertex of the boundaries.
In the real world, the driver has a physical size and the cabinet requires that the driver sit away from the boundaries. This prevents the existence of a perfectly omni-directional polar pattern and the reflections are delayed by a small amount. This seems pretty simple, but I've always been surprised by just how different an outdoor 1/8 space looks from an outdoor 1/2 space measurement. I wish I had some electronic copies to share as it is really quite surprising. Anyways, the point is that the difference in behavior is not at all trivial (we're talking like +-3dB at least).
When you put the sub in the corner of your room, you're always going to see the same 1/8 space behavior, but it gets a bit more complicated because you have a ceiling, and extra walls to deal with. Some of the reflection paths will be long, and some of the reflection paths will be short. When they're short, our ears perceive it as part of the direct sound and so we hear the dips/peaks that it introduces. When they're long, our ears perceive it as part of the natural sound of the room - so the dips/peaks aren't necessarily perceived.
So is the ceiling a part of the boundary or room response? Well I think it will depend on the frequency in question. I think the real question should be, "is the delay long enough to be perceived as part of the natural sound of the room, or is the delay short enough to be perceived as part of the direct sound from the driver?" I think answering that question in context of a specific situation should likely reveal the best path to a solution.
And then another behavior to throw out there...
When you have reflections in the room, there is a good chance that many of those reflections will find their way back to the driver itself. Increasing the air pressure in front of the driver will improve the coupling of the driver. Likewise, decreasing the pressure in front of the driver will reduce its coupling. Horns basically work on the principal of providing more pressure in front of the driver so that more power gets transferred. In fact, it is this behavior that creates the 12dB/octave room gain that we observe - basically, the wavelengths are long enough such that the reflections are in phase with the driver - thereby increasing the amplitude in front of the driver and increasing its coupling. As you go lower, you get more and more in phase (since the phase rotates slower and the time of the reflections are fixed). Things can get real complicated real fast when you consider all the reflection paths that might improve or reduce the coupling of the driver. So in a case of a horn, I'd call those "reflections" as happening early and therefore being perceived as part of the direct sound. In the case of the 12dB/octave room gain of the room, that behavior is going to be delayed by quite a bit since the sound has gotta slosh around the room for a bit to capture the full effect. We also naturally hear the power response of the room with no music playing either, which just reinforces our perception of it being more of a "reverb" than a "direct sound".
All that said, I don't think there is any way to easily determine what would constitute an ideal target response for a given measurement in a particular location. I might suggest that it's easier to think of it in terms of "boundary gain" vs "room gain", but in reality it's going to be a continuum of both - and the fact that it is a continuum makes it real hard to draw lines. But really, it may not be necessary since there is only so much we can, or are willing, to do....in which case it is important to be aware of how we perceive the sound so that we don't make unintentional sacrifices.