You do need a fluid solver at some level, but the fancy stable fluids sims that you see running on GPUs don't have enough resolution to capture the really important elements of the atmosphere/oceans that we see and they are defined in a nice linear space, for the most part. The big drivers of air/ocean circulation here on Earth are differential heating of the sphere and rotation of the sphere. The emergent effects that are really important for local climates like the Gulf Stream and Deep Ocean Circulation don't show up until you start modeling at high resolution and multiple vertical layers in both air and sea.
I am told that some pretty big weather models will run on a PC these days, but they are fairly slow. Weather is not quite the same thing as climate, but if you run weather long enough (and if the sim doesn't start to go stupid), you'll eventually be able to get enough information to generate climate. What I described above was some heuristics that could work quickly on a basic grid and cast in terms of simple graphics primitives that I already have available to me. I was also looking for something that can operate as a pretty simple cellular automaton. If you're sticking to a pure Earth-style model and not wanting a general model, then the latitude bands of Hadley and Ferrel circulation are roughly fixed. That gets you ballpark moisture amounts and mostly what's left is heat transport and inland-coast distances. If I had a few days, I'd code up something based on pure heuristics, but that doesn't seem likely any time soon.