  Accurately reproducing the physics behind the detonations of Type Ia
supernovae and the resultant nucleosynthetic yields is important for
interpreting observations of spectra and remnants. The scales of the processes
involved span orders of magnitudes, making the problem computationally
impossible to ever fully resolve in full star simulations in the present and
near future. In the lower density regions of the star, the curvature of the
detonation front will slow the detonation, affecting the production of
intermediate mass elements. We find that shock strengthening due to the density
gradient present in the outer layers of the progenitor is essential for
understanding the nucleosynthesis there, with burning extending well below the
density at which a steady-state detonation is extinct. We show that a complete
reaction network is not sufficient to obtain physical detonations at high
densities and modest resolution due to numerical mixing at the unresolved
reaction front. At low densities, below 6$\times$10$^{5}$ g cm$^{-3}$, it is
possible to achieve high enough resolution to separate the shock and the
reaction region,and the abundance structure predicted by fully resolved
quasi-steady-state calculations is obtained. For our best current benchmark
yields, we utilize a method in which the unresolved portion of Lagrangian
histories are reconstructed based on fully resolved quasi-steady-state
detonation calculations. These computations demonstrate that under-resolved
simulations agree approximately, $\sim$10\% in post-shock values of
temperature, pressure, density, and abundances, with expected detonation
structures sufficiently far from the under-resolved region, but that there is
still room for some improvement in the treatment of subgrid reactions in the
hydrodynamics to before better than 1$\%$ can be achieved at all densities.
