The blue whirl is a small, stable, spinning blue flame that evolved spontaneously in laboratory experiments while studying, violent, turbulent fire whirls. The blue whirl cleanly burns heavy, liquid hydrocarbon fuels with no soot production, presenting a new potential way for low-emission combustion... It is reproducible, appears for a range of different fuels and initial conditions, is quiet, appears laminar, and has characteristics which led to the idea that it results from vortex breakdown in whirling, reacting fluid. Since its discovery, considerable effort has been put into measurements, which have shown its temperature structure and sensitivity to the boundary layer near the surface. This has led to considerable speculation about the type of flames that comprise it. Simultaneously, there was a numerical effort to study its structure by performing simulations of vortex breakdown in gaseous reactive flows. The simulations described in this paper show that the stable blue whirl is composed of three different flame structures -- a diffusion flame and a premixed rich and lean flame -- all of which meet in a fourth structure, a triple flame which appears as a whirling blue ring. In addition, the blue whirl structure emerges as the result of vortex breakdown in a swirling reactive flow, as evidenced in the simulation by a bubble mode that is usually invisible in the experiments but at the center of the whirl. This paper also presents the tool used for the study and discusses how this might be used for future investigations. (read more)