You know, that might help explain how spectacularly bad GGDT is for high speed flows. However, when I wrote my own toy program a while ago making the same assumptions you do, its performance diverged markedly from that of GGDT at the speeds where compressible effects became important, indicating that GGDT may not be quite as primitive as you suspect.
He does something different than what I do, definitely, but he doesn't solve PDEs unless I'm reading him and his code wrong.
I found a PM from two years ago where I asked D_Hall if he assumes the temperature in the barrel is independent of the location, and he verified that he does. Old GGDT source code seems to further verify this. Unless I'm misreading him and his code, he solves ODEs. You can ask him for further clarification.
I personally don't put much stock into what GGDT does. A lot of the assumptions (even at low speeds) behind GGDT are false. For example, the critical pressure ratio of a valve is generally far lower than what the theory for an orifice might suggest. See this book for some discussion about this.
We need to develop new models to take into account the high-speed phenomena and actively highlight inaccurate parts of the model. Rag made some progress into this a while ago, but I'm not sure what he did with his model (which is based on the method of characteristics, an approach I reject because it's kinda confusing).
Compressible effects are becoming noticeable at even 100m/s, very slow for a modern pneumatic, and at between 200 and 300m/s simply cannot be ignored if reasonable accuracy is desired.
I agree. But, for the low-speed case, especially if the dimensions of the gun are right, the wave dynamics can be ignored. The compressibility effects on gas properties can not be ignored.
I was actually thinking more about common low-speed pneumatics when I wrote what you were replying to, so don't read too far into what I said. The spud gun hobby is bigger than the more dedicated folks at SpudFiles. Most spud gunners don't make high speed guns. Perhaps I should have been more explicit.
Anyhow, I think I might write a Lagrangian code now... you've got me interested in this again.