) ad hoc
to reproduce the observations. Various parameterizations of this type
of model were proposed. They agree on a turbulent speed of 30% speed of
sound. Initiated once, the flame becomes circonvoluée because of the turbulence produced by instabilities of the flame.
Combustion continues until a transition towards a detonation (the model of delayed detonation that we will describe further) or until the flame dies out by expansion of the fluid.
Remain to know if this mechanism is sufficiently powerful to allow the dispersion of dwarf white and if the composition and the speed of ejected are compatible with the observations.
The model with a
dimension of fast deflagration (model W7 nomoto1984) is in concord with
the spectra and the lightcurves observed. However, this model rests
on a parameterization of the function turbulent speed () ad hoc
to reproduce the observations. Various parameterizations of this type
of model were proposed. They agree on a turbulent speed of 30% speed of
sound.
Another problem seems to be the overproduction of elements rich in neutrons. In spite of its great successes this type of modeling has always a little evil to reproduce abundances of elements of intermediate mass. The intrinsically turbulent nature of this type of explosion makes modeling in three dimensions essential to reproduce the whole of the effects.
The problem of
modeling à .trois.dimensions is that they are much more difficult to
build. The scales concerned go from the thickness of the flame (of the
order of the centimetre) until the size of dwarf white ( 
being quite lower than the value of 30% speed of sound.
To cure this problem several solutions were brought to the number of which active turbulent combustion and multiple lighting.
An additional turbulence could be due to hydrodynamic instabilities which we saw previously. In particular, instabilities of Rayleigh-Taylor allow an increase in the surface of the flame and thus of the burnup rate and energy production. Figure 5.10 exit of gamezo2003 presents a simulation of a deflagration undergoing this instability which makes it possible to destroy the dwarf white one.
Multiple lighting would have as a virtue to make it possible to burn more fuel with low density, thus making it possible to regulate the problem of nucleosynthesis involved in the models 1D, ii.e., the overproduction of elements rich in neutrons. A simulation due to reinecke2002 is presented figure 5.11 , it shows the evolution of the surface of the flame according to the number of points of lighting.
In conclusion, if the models, by taking into account either the effects of active turbulence, or multiple lighting, or of the effects which had with the instability of Raylegh-Taylor, are able to produce turbulent speeds of about 30%, then they will be in almost complete agreement with the observations. Moreover, it seems that the value speed is completely uncoupled from microscopic physics of the flame on the great scales. The properties would be thus dominated by pure hydrodynamic effects and would make thus the mechanism intrinsically robust.
The accretion rate of the progenitor, the number and the localization of lightings have a significant influence however and could be an interesting explanation to account for the variety of the supernovæ of the type Ia. Enfin, potentially, all these effects can also depend on the composition and metalicity, which would explain the correlation between the stellar population and the power of the explosion.