Modeling Weather in a non-Earthlike setting

I'm trying to design, in collaboration with friends who actually understand at least the astrophysics involved, a setting physically located within an O'Neill cylinder, and we've collectively run into a stumbling block regarding weather. Is there a way of constructing a mathematical model to at least get approximate ground wind speed for a large cylinder of air heated at one end (and in strips along the sides)? I don't even know what field to consider it, let alone how to approach the problem, but I'd like to at least make sure the size we picked won't result in constant tornadoes.

modern meteorological tools may not be designed for it; but they should be able to give you some decent estimates if you can find someone with them. At a college there should be some people who'd have the necessary software to give some estimates.
I'm not an expert; but I imagine the people who thought it up would at least be vaguely aware of wind potential. How big is this thing? if it's sized as per the ones in the article; i'd guess it's small enough that wind would mostly be in the gentle breeze category; it's just not big enough to support sustained high winds as long as there's mostly open airflow.
You could get some computer scientist to make a very basic model with several billion nodes; and let it run through basic convection transfers to get some estimates.

Fieldwise, it's a subset of physics; thermodynamics would provide the info you need; meteorology would also.

In an artifical structure, tornados shouldn't be a problem; it's far too easy to mess with airflow enough to prevent that from occurring (even if I don't know how, engineers in that world with the tech to build such a structure would surely learn how to make good windbreaks)

Now if the cylinder were planet-sized; then I really don't know. and it'd depend on where gravity came from too.

also, wind speed will vary alot based on a host of factors about how everything is set up;
but with tech high enough to make such things, just assume rule 0 lets them moderate weather well enough.
tldr: find a college, ask a meteorology professor.

It's 30 kilometers in radius, and the cylinder, sans endcaps, is 300 kilometers long. It's rather more a dwarf McKendree cylinder than strictly an O'Neill, but the same physics apply.

And actually, I hadn't thought of asking my computer scientist friend, perhaps because I don't have the physics to figure out the model he'd need to make.

Most of this is going to depend on the locations of your heat syncs. As they're the soul source of colder air, they're going to behave like valleys, while the areas farthest from them are going to have the greatest surplus of heat and will act as thermal mountains.

Most rain will form along the intersection of these two things.

If you go with the version Gundam used, with atmosphere processors and the heat exchangers on the end caps, wing will constantly blow towards the centre of the station, rarely fluctuating because of the limited ability of the landmasses to dump heat into the atmosphere before they roll back into the sunlight.

If you're going for the version of the system that has shuttered nights, it's going to have a cooler period in the early morning, followed by disturbed air for about an hour after the shutters open due to uneven heating.

Most likely, the thing would be temperate at hte ends and tropical in the middle. A cylinder of your dimensions probably needs artificial water redistrobution, otherwise it's going to desertify [assuming you aren't going for a maddeningly complex network of heat conductors].

Who knew living with a guy who designed space station shielding was worth the time?