This solar simulation is a combination of fluid effects, dynamic particle-based sunspots, and custom 3D flare events. There is even an occasional transit by the planet Mercury.
The main geometry is a simple sphere with uvs. In a GLSL shader, I add layers of noise to achieve the base patterns. The positions of the sunspots and solar flares are dictated by a layer of unseen particles that travel around the equatorial belt of the sun. If any two particles gets close enough together they are joined by flare geometry which extends outward until it becomes too long at which point it will dissipate.
An R&D version of this project was made to run on a 60" touchscreen. Upon touching the surface, a sunspot is created. Touch and drag rotates the sun, and touching with two fingers simultaneously created a solar flare arc between your fingers.