Mathematical simulation of turbulent combustion of carbon in the problems of white dwarf mergers and explosions of the type Ia supernovae

Type Ia supernovae play a key role in astrophysics, but the study of the mechanisms of their explosion is still incomplete. The mathematical simulation apparatus is the main one for studying known and all potentially new scenarios of explosion of the type Ia supernovae. All scenarios are based on the nuclear combustion of the white dwarf material, first of all, the nuclear combustion of carbon, and the subsequent detonation with the supernova explosion. For simulation of the explosion of type Ia supernovae, a subgrid model of static carbon combustion is used. This model does not take into account the previous evolution and dynamics of white dwarfs, which leads to lower values of the combustion energy and, consequently, the supernova explosion energy. A mathematical model of the turbulent combustion of carbon is proposed, which more adequately describes the material combustion taking into account the white dwarfs dynamics. Using computational experiments, it is shown that the supersonic turbulent combustion allows increasing the explosion energy by several times. This is achieved by «pumping» the kinetic energy obtained due to the nonzero velocity dispersion into internal energy and by more active course of nuclear reactions of the alpha-chain from carbon to iron and nickel. In the future, the constructed model will be used as a subgrid model of the combustion of the white dwarf material.