Numerical simulation of low Mach number reacting flows

The explosion of a Type Ia supernova (SNIa) begins as a turbulent flame deep within a 1.4 solar-mass white dwarf. Initially the burning happens in the flamelet regime where turbulence only serves to wrinkle and fold an essentially laminar burning front. However, as the star expands and the flame moves outwards, it encounters regions of lower density. At ∼ 2 × 10g cm, the flame transitions to a distributed burning regime. Here individual flamelets are disrupted by turbulent eddies, resulting in a fundamental change in the character of the burning. Detonation does not occur immediately because the turbulently broadened flamelets are still too thin. As the density declines further, however, each flamelet thickens and moves faster until only a few structures are contained within the ∼ 10 km integral scale of the SN turbulence. It is here that detonation may occur. We present simulations using both a three-dimensional low Mach number model and a one-dimensional linear eddy model to explore the structure of these flames and quantify their scaling behavior. Our results suggest that detonation may be possible at a density near 1.0× 10 g cm.