A 2D Discrete Surface Flux Transport (DSFT) model applied to polar and quiet sun regions.

We have developed a Surface Flux Transport simulation utilizing a Semi-Lagrangian scheme to advect discrete magnetic flux elements. Advection occurs due to the flow fields from supergranulation, meridional flow, and differential rotation. Granular advection is modeled using a time integrated effect which lowers the computational cost of the simulation. We have incorporated observational, energetic and geometric considerations in constructing the magnetic flux dynamics of emergence, interaction, and fragmentation. Our model reproduces observed distributions of magnetic flux in quiet sun and at the poles. The variation of mean squared velocities with flux is also reproduced. Our simulation clarifies which processes are essential in reproducing the dynamics of solar magnetic flux balance.