For realistic solar cycle simulations, corresponding inputs have to be modeled and fed to the Surface flux transport code.
The modelling was done with reference to the study carried out by Jie Jiang et al. (http://arxiv.org/abs/1102.1266v1) and van Ballegooijen et al. 1998.
The input parameters needed are:
(1) Time of BMR eruption
(2) Latitude of eruption
(3) Tilt angle (with respect to the solar equator)
(4) Longitude of eruption
(5) Radius of individual spots in a BMR
(6) Peak magnetic field (Bmax)
(7) Separation between the centers of the individual spots.
One solar cycle of 11 years was divided in 120 phases. And the sunspots were placed at their respective locations after each phase. The following figure shows the latitude of eruption(in degrees) vs phase that was fed into the surface flux transport code:
An initial polar field of +-4.5 Gauss was placed within 23 degrees of the poles, and the surface flux transport code was given a run for 12 sunspot cycles(132 years). This is what was the output:
This is again a butterfly diagram, but you can really see butterfly like structures in it. The polar magnetic field reversal is clearly evident from the diagram.
But, the problem here is, the magnitude of the peak polar field is not constant. It varies from cycle to cycle.
No. of Cycle Peak Magnetic field in the northern hemisphere