  Type Ia supernovae (SNe Ia) are one of the major tools to determine the
cosmological parameters. Utilizing them as distance indicators, it is possible
to geometrically survey the universe. To this end, the intrinsic scatter in the
luminosities of these events needs to be calibrated using empirical relations
between observables. A theoretical explanation for these relations is still
lacking and can only be provided by a sound understanding of the mechanism of
SNe Ia. Recently there has been significant progress in modeling SNe Ia. We
report on numerical simulations of the explosion process, compare the results
with observations of nearby SNe Ia, and discuss current uncertainties of the
models. The presented simulations shed some light on the origin of the
diversity of SNe Ia. Such simulations will pave the way towards an
understanding of SN Ia diversities and correlations of their properties and
ultimately provide a tool to validate the cosmological implications of SN Ia
distance measurements.
