  Simulating detonations in astrophysical environments is often complicated by
numerical approximations to shock structure. A common prescription to ensure
correct detonation speeds and associated quantities is to prohibit burning
inside the numerically broadened shock (Fryxell et al. 1989). We have performed
a series of simulations to verify the efficacy of this approximation and to
understand how resolution and dimensionality might affect its use. Our results
show that, in one dimension, prohibiting burning in the shock is important
wherever the carbon burning length is not resolved, in keeping with the results
of Fryxell et al. (1989). In two dimensions, we find that the prohibition of
shock burning effectively inhibits the development of cellular structure for
all but the most highly-resolved cases. We discuss the possible impacts this
outcome may have on sub-grid models and detonation propagation in models of
Type Ia supernovae, including potential impacts on observables.
