[jlhawn]

The title should be updated to note this is from 2006.

Has there been anything like this published in the past 20 years but for compressible fluids? I have wanted to make a simple atmospheric model for years but have been unable to because of the complexity and probably my lack of complete understanding.

[btrettel]

Fluid dynamicist here. The word "compressible" has multiple meanings and this might be confusing you. You don't need compressible flows in the sense of high Mach numbers. There are other models where the flow is variable density, but thermodynamic and hydrodynamic pressure are decoupled to remove the pressure waves that make high Mach number flows hard. There's also the Boussinesq approximation for buoyancy when the density varies only a small amount. I'm not particularly familiar with atmospheric models, but I'm sure they don't use the high Mach number form. "Incompressible" methods are common for the second class of model I mentioned, though how to use them so might not be obvious.

[bestouff]

Something like this ? https://github.com/bestouff/weather_simulation

[lacunary]

I'm curious what you want to model; what's an example phenomenon you'd like to be able to demonstrate?

[jlhawn]

Atmospheric circulation. hadley cell, polar cell, and mid-latitude cells. It would also be interesting to see how new bands would occur if we increased the rotational speed of the earth, thus increasing the strength of the coriolis effect. It would also be neat to draw your own continents and orography and see how that impacts climate. which places become more wet/dry, etc. Change how much long wave radiation is absorbed by the atmosphere as the composition of the atmosphere changes. I'm not interested in actually making weather or climate predictions but using it as a tool to educate people on how the climate works.

[jamiejquinn]

Interestingly, most large-scale atmospheric models I know of use a (mostly) incompressble fluid approximation, even though air is obviously compressible at human scales. It just isn't at the flow speeds and length scales of global-scale fluid models. Where compressibility is important for those models is where density changes due to temperature. Look into the Boussinesq and anelastic approximations if you're interested!

[jlhawn]

that's interesting because my understanding was that a lot of models used pressure as the vertical (height) coordinate and with tracking temperature at any given coordinate lets you know the density of the air at any point.

[jamiejquinn]

That's typical of models that use the anelastic approximation, where it's useful for a number of reasons to rewrite the equations replacing the true vertical with a vertically stratified variable. I've seen density, pressure and temperature used.

That's less of a different model and more a different way to rewrite the equations to make them easier to analyse or simulate.

We might be talking at slightly different angles here. There's a strong difference in the equations between compressibity of the fluid due to compression and changes in density due to temperature, chemical concentration, etc. The term compressibility usually refers to the first usage, and modelling it leads to sound waves in the system and has major implications for how the system is simulated, I mean it's an entirely different class of algorithms. The second, where density still changes but not due to compression, so no sound waves, that can be easily modelled without including full compressibility. This allows (generally simpler) incompressible models to still incorporate useful thermal physics where important, like in climate and weather. Also, the smaller the scale of the system the more compressibility matters so I wouldn't be surprised if compressibility starts to matter for e.g. Tornados. But I'm not certain on that...