  The propagation of cellularly stabilized thermonuclear flames is investigated
by means of numerical simulations. In Type Ia supernova explosions the
corresponding burning regime establishes at scales below the Gibson length. The
cellular flame stabilization - which is a result of an interplay between the
Landau-Darrieus instability and a nonlinear stabilization mechanism - is
studied for the case of propagation into quiescent fuel as well as interaction
with vortical fuel flows. Our simulations indicate that in thermonuclear
supernova explosions stable cellular flames develop around the Gibson scale and
that deflagration-to-detonation transition is unlikely to be triggered from
flame evolution effects here.
