On the Small-scale Stability of Thermonuclear Flames in Type Ia Supernovae

We present a numerical model which allows us to investigate thermonuclear flames in Type Ia supernova explosions. The model is based on a finite-volume explicit hydrodynamics solver employing PPM. Using the level-set technique combined with in-cell reconstruction and flux-splitting schemes we are able to describe the flame in the discontinuity approximation. We apply our implementation to flame propagation in Chandrasekhar-mass Type Ia supernova models. In particular we concentrate on intermediate scales between the flame width and the Gibson-scale, where the burning front is subject to the Landau-Darrieus instability. We are able to reproduce the theoretical prediction on the growth rates of perturbations in the linear regime and observe the stabilization of the flame in a cellular shape. The increase of the mean burning velocity due to the enlarged flame surface is measured. Results of our simulation are in agreement with semianalytical studies. Subject headings: hydrodynamics—instabilities—supernovae:general—turbulence