  Fractal mesh refinement enables mesh refinement regimes to the Gibson scale
and beyond. Conventional multifractal subgrid models have cost considerations
which also lead to local mesh refinement, but more importantly, the application
of these models to compressible turbulent deflagration fronts is a topic for
future research, while subgrid models tuned to this complex physics lack a
multifractal search focus, and for cost reasons do not allow the large search
volumes required to find the sought for rare event to trigger a DDT.
  Here we propose methods to resolve fine scales and locate rare possible DDT
trigger events within large volumes while addressing multifractal issues at a
feasible computational cost. We are motivated by the goal of confirming or
assessing the hypothesis of a delayed detonation in type Ia supernova and to
assessing the delay in this event if it is found to occur.
