Type Ia supernovae (SNe Ia) are the most powerful thermonuclear explosions in the Universe and their light curves serve as a valuable "standard candle" for the cosmologists. The standard astrophysical scenario is that of an exploding white dwarf star; however, a comprehensive theoretical model of the mechanism is still lacking. Recent advances in computational power and numerical techniques have facilitated three-dimensional simulations of these events -- and raised numerous questions. The thermonuclear flame that gives rise to the explosion of the star resembles premixed combustion where two solutions - detonation and deflagration - are admissible. From observational constraints it is clear that the flame starts out as a sub-sonic deflagration. Consequently, one of the outstanding problems is to determine, whether this flame, accelerated by turbulence, leads to explosions energetic enough to be consistent with observations, or whether a later transition to a supersonic detonation is both possible and necessary. In the freely expanding medium of a SN Ia explosions, such transitions are difficult to achieve.
Previous studies of the ignition process supported by SciDAC suggest that the initial flame may ignite in only a few patches, near the center on one side of the star. These bubbles of ash begin a quick ascension to the surface. If the energy release due to burning in transit is small, the star could stay gravitationally bound until after they break out. Collisions between laterally expanding regions of fuel and ash could, in principle, give rise to a "gravitationally confined detonation" as has been suggested by the DOE Chicago FLASH Center. We present models in which the flame is represented in a level-set approach and the effects of turbulence on the flame are included in a sub-grid scale model. This method allows one to follow, for the first time, the evolution of the burning bubbles resulting from different initial set-ups in three-dimensional simulations. We explore several configurations and discuss the question of whether detonation could occur as the two-dimensional simulations at Chicago suggest.