have intensively addressed these issues (e.g., Reinecke et al. 2002; Gamezo et al. 2003; Röpke & Hillebrandt 2005; Bravo & García-Senz 2006; Röpke et al. 2006b; Schmidt & Niemeyer 2006). With high resolution multi-dimensional hydrodynamic simulations, coupled with an appropriate sub-grid model to capture turbulence effects on unresolved scales, recent studies provide essentially “parameter-free” simulations for the initial deflagration stage, where only the structure of the pre-supernova WD and the distribution of the initial deflagration ignition sparks set up the initial conditions.

The multi-dimensional simulations have been performed with different initial conditions to see if SNe Ia in general can be explained in a framework of a pure deflagration explosion, as is summarized by Röpke et al. (2007b). Detailed nucleosynthesis calculations have been performed for some deflagration models (Travaglio et al. 2004a, 2005; Kozma et al. 2005, Röpke et al. 2006a). These studies indicate that the pure deflagration explosion can explain a part of SNe Ia, up to relatively weak and faint SNe Ia in the normal population. However, it has also been shown that a subsequent detonation phase is probably necessary to account for typical normal SNe Ia and brighter ones (Gamezo et al. 2005; Röpke et al. 2007b).

