  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.
