Context :

Aims : Deflagration models poorly explain the observed diversity of SNIa .
Current multidimensional simulations of SNIa predict a significant amount of , so far unobserved , carbon and oxygen moving at low velocities .
It has been proposed that these drawbacks can be resolved if there is a sudden jump to a detonation ( delayed detonation ) , but these kinds of models have been explored mainly in one dimension .
Here we present new three-dimensional delayed detonation models in which the deflagraton-to-detonation transition ( DDT ) takes place in conditions like those favored by one-dimensional models .

Methods : We have used a smoothed-particle-hydrodynamics code adapted to follow all the dynamical phases of the explosion , with algorithms devised to handle subsonic as well as supersonic combustion fronts .
The starting point was a centrally ignited C-O white dwarf of 1.38 \mathrm { M } _ { \sun } .
When the average density on the flame surface reached \sim 2 - 3 \times 10 ^ { 7 } g cm ^ { -3 } a detonation was launched .

Results : The detonation wave processed more than 0.3 M _ { \sun } of carbon and oxygen , emptying the central regions of the ejecta of unburned fuel and raising its kinetic energy close to the fiducial 10 ^ { 51 } ergs expected from a healthy Type Ia supernova .
The final amount of \@element [ ] [ 56 ] [ ] [ ] { \mathrm { Ni } } synthesized also was in the correct range .
However , the mass of carbon and oxygen ejected is still too high .

Conclusions : The three-dimensional delayed detonation models explored here show an improvement over pure deflagration models , but they still fail to coincide with basic observational constraints .
However , there are many aspects of the model that are still poorly known ( geometry of flame ignition , mechanism of DDT , properties of detonation waves traversing a mixture of fuel and ashes ) .
Therefore , it will be worth pursuing its exploration to see if a good SNIa model based on the three-dimensional delayed detonation scenario can be obtained .