  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.
