Supernovae are such bright objects that they can be observed even at high redshifts. Some types of such events, for example, type Ia (thermonuclear), have peculiarities of the light curve, which allows them to be used for cosmological applications. The light curve is determined by the details of the explosion dynamics and nucleosynthesis: in particular, it depends on the amount of iron-peak elements produced during the explosion. We discuss the burning processes in such objects and the peculiarities of turbulence simulations in them, which is needed for a proper hydrodynamic description of the explosion process. A direct nucleosynthesis calculation is performed for the temperature and density profiles derived in the available 3D hydrodynamic explosion simulations. We show that in the supernova progenitor model considered the calculated abundances of elements from carbon to iron-peak elements are in good agreement both with the observations and with the calculations of other authors. At the same time, no r-elements are produced even at the maximum neutron excess for this model (Ye ~ 0.47) due to the slow evolution of the density and temperature.