  The emergence of tilted bipolar active regions and the dispersal of their
flux, mediated via processes such as diffusion, differential rotation and
meridional circulation is believed to be responsible for the reversal of the
Sun's polar field. This process (commonly known as the Babcock-Leighton
mechanism) is usually modeled as a near-surface, spatially distributed
$\alpha$-effect in kinematic mean-field dynamo models. However, this
formulation leads to a relationship between polar field strength and meridional
flow speed which is opposite to that suggested by physical insight and
predicted by surface flux-transport simulations. With this in mind, we present
an improved double-ring algorithm for modeling the Babcock-Leighton mechanism
based on active region eruption, within the framework of an axisymmetric dynamo
model. Using surface flux-transport simulations we first show that an
axisymmetric formulation -- which is usually invoked in kinematic dynamo models
-- can reasonably approximate the surface flux dynamics. Finally, we
demonstrate that our treatment of the Babcock-Leighton mechanism through
double-ring eruption leads to an inverse relationship between polar field
strength and meridional flow speed as expected, reconciling the discrepancy
between surface flux-transport simulations and kinematic dynamo models.
