It's called chaos, or sensitivity to initial conditions. And also, you are comparing chalk to cheese. The black hole model is attempting to model possible behaviour of gas (plasma, surely!) in that environment, and to deduce some average properties such as its temperature. Weather forecasting is an attempt to predict exactly what state the atmoshere will be in tomorrow or next week, given observations of what state it's in today. A black hole type model simply tells you that it's possible that somewhere on the planet you will find a square mile where the air temperature is 40C and the humidity is high. And that nowhere will you find such a square mile where the temperature is 80C.
The weather forecast model is chaotic, or sensitive. You can't measure the atmosphere's current state with complete accuracy. The measurement errors grow with simulated time, to a greater or lesser extent, until the model is wholly erroneous when compared to the later reality. (It still represents possible weather, just not the correct realisation thereof). On the bright side, your forecast for a week out is useful maybe two times in three, and that for two weeks out is a waste of computer time. In the worst case, the not-quite-hurricane that is going to devastate northern France in six hours' time does a sudden right-angled turn and devastates Southern England instead. (Michael Fish, you are forgiven).