  We develop an improved method for tracking the nuclear flame during the
deflagration phase of a Type Ia supernova, and apply it to study the variation
in outcomes expected from the gravitationally confined detonation (GCD)
paradigm. A simplified 3-stage burning model and a non-static ash state are
integrated with an artificially thickened advection-diffusion-reaction (ADR)
flame front in order to provide an accurate but highly efficient representation
of the energy release and electron capture in and after the unresolvable flame.
We demonstrate that both our ADR and energy release methods do not generate
significant acoustic noise, as has been a problem with previous ADR-based
schemes. We proceed to model aspects of the deflagration, particularly the role
of buoyancy of the hot ash, and find that our methods are reasonably
well-behaved with respect to numerical resolution. We show that if a detonation
occurs in material swept up by the material ejected by the first rising bubble
but gravitationally confined to the white dwarf (WD) surface (the GCD
paradigm), the density structure of the WD at detonation is systematically
correlated with the distance of the deflagration ignition point from the center
of the star. Coupled to a suitably stochastic ignition process, this
correlation may provide a plausible explanation for the variety of nickel
masses seen in Type Ia Supernovae.
