I have a flat world where the parent star, a sizeably small star, travels around the world. The world is covered by a dome that provides its atmosphere and the star is outside of this. The star travels over the dome giving the world its daytime and when it travels under the belly of the world that is night, until it rises again on the sunrise side. The flat world itself also turns but slowly. It's not too dissimilar to the Discworld, really.
My question is, though, what might the weather be like? Are weather patterns really more in the control of the terrain than the nature of a star's travel?
I hope that makes sense and help would be very much appreciated. I've had the world for years but I'm finally trying to figure out the weather, including seasons.