  In thermonuclear supernovae, intermediate mass elements are mostly produced
by distributed burning provided that a deflagration to detonation transition
does not set in. Apart from the two-dimensional study by Roepke & Hillebrandt
(2005), very little attention has been payed so far to the correct treatment of
this burning regime in numerical simulations. In this article, the physics of
distributed burning is reviewed from the literature on terrestrial combustion
and differences which arise from the very small Prandtl numbers encountered in
degenerate matter are pointed out. Then it is shown that the level set method
continues to be applicable beyond the flamelet regime as long as the width of
the flame brush does not become smaller than the numerical cutoff length.
Implementing this constraint with a simple parameterisation of the effect of
turbulence onto the energy generation rate, the production of intermediate mass
elements increases substantially compared to previous simulations, in which the
burning process was stopped once the mass density dropped below 10^7 g/cm^3.
Although these results depend on the chosen numerical resolution, an
improvement of the constraints on the the total mass of burning products in the
pure deflagration scenario can be achieved.
