A localised subgrid scale model for fluid dynamical simulations in astrophysics

Abstract

The dynamics of the explosive burning process is highly sensitive to the flame speed model in numerical simulations of type Ia supernovae. Based upon the hypothesis that the effective flame speed is determined by the unresolved turbulent velocity fluctuations, we employ a new subgrid scale model wh ich includes a localised treatment of the energy transfer th rough the turbulence cascade in combination with semi-statistical closures for the dissipation and non-local transport of t urbulence energy. In addition, subgrid scale buoyancy effects are included. In the limit of negligible energy transfe r and transport, the dynamical model reduces to the Sharp-Wheeler relation. According to our findings, the Sharp-Wheeler relation is insu ffcient to account for the complicated turbulent dynamics of flames i n thermonuclear supernovae. The application of a co-moving grid technique enables us to achieve very high spatial resolution in the burning region. Turbulence is produced mostly at the flame surface and in the interior ash regions. Consequently, ther e is a pronounced anisotropy in the vicinity of the flame front s. The localised subgrid scale model predicts significantly enhan ced energy generation and less unburnt carbon and oxygen at low velocities compared to earlier simulations.