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.
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