  Some simulations of Type Ia supernovae feature self-consistent thermonuclear
detonations. However, these detonations are not meaningful if the simulations
are not resolved, so it is important to establish the requirements for
achieving a numerically converged detonation. In this study we examine a test
detonation problem inspired by collisions of white dwarfs. This test problem
demonstrates that achieving a converged thermonuclear ignition requires spatial
resolution much finer than 1 km in the burning region. Current computational
resource constraints place this stringent resolution requirement out of reach
for multi-dimensional supernova simulations. Consequently, contemporary
simulations that self-consistently demonstrate detonations are possibly not
converged and should be treated with caution.
