On the applicability of the level set method beyond the flamelet regime in thermonuclear supernova simulations

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 Röpke & 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 107 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.