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The dynamics of the explosive burning process is highly sensitive to theflame speed model in numerical simulations of type Ia supernovae. Based uponthe hypothesis that the effective flame speed is determined by the unresolvedturbulent velocity fluctuations, we employ a new subgrid scale model whichincludes a localised treatment of the energy transfer through the turbulencecascade in combination with semi-statistical closures for the dissipation andnon-local transport of turbulence energy. In addition, subgrid scale buoyancyeffects are included. In the limit of negligible energy transfer and transport,the dynamical model reduces to the Sharp-Wheeler relation. According to ourfindings, the Sharp-Wheeler relation is insuffcient to account for thecomplicated turbulent dynamics of flames in thermonuclear supernovae. Theapplication of a co-moving grid technique enables us to achieve very highspatial resolution in the burning region. Turbulence is produced mostly at theflame surface and in the interior ash regions. Consequently, there is apronounced anisotropy in the vicinity of the flame fronts. The localisedsubgrid scale model predicts significantly enhanced energy generation and lessunburnt carbon and oxygen at low velocities compared to earlier simulations.

A localised subgrid scale model for fluid dynamical simulations in astrophysics