  We refine our previously introduced parameterized model for explosive
carbon-oxygen fusion during thermonuclear supernovae (SN Ia) by adding
corrections to post-processing of recorded Lagrangian fluid element histories
to obtain more accurate isotopic yields. Deflagration and detonation products
are verified for propagation in a uniform density medium. A new method is
introduced for reconstructing the temperature-density history within the
artificially thick model deflagration front. We obtain better than 5\%
consistency between the electron capture computed by the burning model and
yields from post-processing. For detonations, we compare to a benchmark
calculation of the structure of driven steady-state planar detonations
performed with a large nuclear reaction network and error-controlled
integration. We verify that, for steady-state planar detonations down to a
density of 5x10^6 g/cc, our post processing matches the major abundances in the
benchmark solution typically to better than 10% for times greater than 0.01 s
after the shock front passage. As a test case to demonstrate the method,
presented here with post-processing for the first time, we perform a two
dimensional simulation of a SN Ia in the Chandrasekhar-mass
deflagration-detonation transition (DDT) scenario. We find that reconstruction
of deflagration tracks leads to slightly more complete silicon burning than
without reconstruction. The resulting abundance structure of the ejecta is
consistent with inferences from spectroscopic studies of observed SNe Ia. We
confirm the absence of a central region of stable Fe-group material for the
multi-dimensional DDT scenario. Detailed isotopic yields are tabulated and only
change modestly when using deflagration reconstruction.
