  The paper describes a physical model and numerical algorithm for modeling
Type Ia supernova (SNIa) explosions in three dimensions and presents first
results of modeling a deflagration explosion in a nonrotating,
Chandrasekhar-mass carbon-oxygen (CO) white dwarf. Simulations show that the
turbulent flame speed grows exponentially, reaches approximately 30% of the
speed of sound, and then declines as the large-scale turbulence is frozen by
expansion. The freezing of turbulent motions appears to be a crucial physical
mechanism regulating the rate of deflagration in SNIa. The energy of the
explosion is comparable to that of a typical SNIa. However, the presence of the
outer layer of unburned CO and the formation of intermediate mass elements and
pockets of unburned CO near the center pose problems for the modeling of SNIa
spectra. Delayed detonation is a way to alleviate these problems and to produce
consistent spectra.
