Supernovae of type Ia (SNe Ia) are very important for cosmography. To exclude systematic effects in linking the observed light of distant SNe Ia to the parameters of cosmological models, one has to understand the nature of supernova outbursts and to build accurate algorithms for predicting their emission. We review the recent progress of modeling the propagation of nuclear flame subject to numerous hydrodynamic instabilities inherent to the flame front. The Rayleigh-Taylor (RT) instability is the main process governing the corrugation of the front on the largest scales, while on the smallest scales the front propagation is controlled by the Landau-Darrieus instability. Based on several hydrodynamic explosion models, we predict the broad-band UBVI and bolometric light curves of SNe Ia, using our 1D-hydro code which models multi-group time-dependent non-equilibrium radiative transfer inside SN ejecta. We employ our new corrected treatment for line opacity in the expanding medium, which is important especially in UV and IR bands. The results are compared with the observed light curves. Especially interesting is a recent 3D-deflagration model computed at MPA, Garching, by M. Reinecke et al.
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