A promising model for normal Type Ia supernova (SN Ia) explosions are delayeddetonations of Chandrasekhar-mass white dwarfs, in which the burning starts outas a subsonic deflagration and turns at a later phase of the explosion into asupersonic detonation. The mechanism of the underlyingdeflagration-to-detonation transition (DDT) is unknown in detail, but necessaryconditions have been determined recently. The region of detonation initiationcannot be spatially resolved in multi-dimensional full-star simulations of theexplosion. We develop a subgrid-scale (SGS) model for DDTs in thermonuclearsupernova simulations that is consistent with the currently known constraints.The probability for a DDT to occur is calculated from the distribution ofturbulent velocities measured on the grid scale in the vicinity of the flameand the fractal flame surface area that satisfies further physical constraints,such as fuel fraction and fuel density. The implementation of our DDT criterionprovides a solid basis for simulations of thermonuclear supernova explosions inthe delayed detonation scenario. It accounts for the currently known necessaryconditions for the transition and avoids the inclusion of resolution-dependentquantities in the model. The functionality of our DDT criterion is demonstratedon the example of one three-dimensional thermonuclear supernova explosionsimulation.
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