  Type Ia supernovae (SNe Ia) are a prime tool in observational cosmology. A
relation between their peak luminosities and the shapes of their light curves
allows to infer their intrinsic luminosities and to use them as distance
indicators. This relation has been established empirically. However, a
theoretical understanding is necessary in order to get a handle on the
systematics in SN Ia cosmology. Here, a model reproducing the observed
diversity of normal SNe Ia is presented. The challenge in the numerical
implementation arises from the vast range of scales involved in the physical
mechanism. Simulating the supernova on scales of the exploding white dwarf
requires specific models of the microphysics involved in the thermonuclear
combustion process. Such techniques are discussed and results of simulations
are presented.
