  Modeling type Ia supernova (SN Ia) explosions in three dimensions allows to
eliminate any undetermined parameters and provides predictive power to
simulations. This is necessary to improve the understanding of the explosion
mechanism and to settle the question of the applicability of SNe Ia in
cosmological distance measurements. Since the models contain no tunable
parameters, it is also possible to directly assess their validity on the basis
of a comparison with observations. Here, we describe the modeling of SNe Ia as
thermonuclear explosions in which the flame after ignition near the center of
the progenitor white dwarf star propagates outward in the sub-sonic
deflagration mode accelerated by the interaction with turbulence. We explore
the capabilities of this model by comparison with observations and show in a
preliminary approach, how such a model can be applied to study the origin of
the diversity of SNe Ia.
