Detonation shock dynamics of type Ia supernovae

The wavefront propagation of curved detonation waves in carbon-oxygen cores and helium shells of type Ia supernova progenitors may be predicted via a Detonation Shock Dynamics (DSD) approach. DSD is used typically in engineering to model explosives. A level set implementation is used to evolve the front, using intrinsic quasi-steady, quasi-one-dimensional detonation speed-curvature relationships. The effects of curvature are analysed for a number of models from the literature which originally use the local planar detonation speed, and compared. The differences can be very profound in the low density regions where detonation models are exploited to produce intermediate mass elements. In detonable low density regions, the detonation wave speed tends to be much lower than the planar DSD analysis predicts, while the subsonic driving zone controlling the dynamics is many order of magnitude shorter than its planar version. However, the lower shock temperatures ensure that the complete reaction lengths are orders of magnitude longer when curvature effects are properly accounted. Furthermore, the material cannot be detonated in sufficiently low density regions due to a curvature induced extinction limit. The implications for and need to reassess the nucleosynthesis, intermediate mass element production and even the progenitors of SN Ia detonation models, is discussed. In the second part of this thesis, an adapted method for evolving the front when the speed function has a curvature component is introduced. A stationary boundary value problem is adapted by considering the non-stationary form. This method is similar in its implementation to the level set form but is more efficient. Its efficiency and error is investigated and compared to the level set method.