  The main objective of this paper is to introduce the STABLE (Surface flux
Transport And Babcock-LEighton) solar dynamo model. STABLE is a 3D
Babcock-Leighton/Flux Transport dynamo model in which the source of poloidal
field is the explicit emergence, distortion, and dispersal of bipolar magnetic
regions (BMRs). Here we describe the STABLE model in more detail than we have
previously and we verify it by reproducing a 2D mean-field benchmark. We also
present some representative dynamo simulations, focusing on the special case of
kinematic magnetic induction and axisymmetric flow fields. Not all solutions
are supercritical; it can be a challenge for the BL mechanism to sustain the
dynamo when the turbulent diffusion near the surface is $\geq 10^{12}$ cm$^2$
s$^{-1}$. However, if BMRs are sufficiently large, deep, and numerous, then
sustained, cyclic, dynamo solutions can be found that exhibit solar-like
features. Furthermore, we find that the shearing of radial magnetic flux by the
surface differential rotation can account for most of the net toroidal flux
generation in each hemisphere, as has been recently argued for the Sun by
Cameron & Schussler (2015).
