  Despite the importance of Type Ia supernovae (SNe Ia) for modern
astrophysics, their detailed mechanism is still not fully understood. In this
contribution, we present recent findings from numerical explosion models in the
context of the observed diversity of SNe Ia and we discuss how these models can
help to shed light on the explosion mechanism and the progenitor stars of SNe
Ia. In addition, we introduce the Heidelberg Supernova Model Archive (HESMA), a
new online data base where we provide integrated isotopic abundances and
radially averaged ejecta profiles and synthetic observables for a wide range of
state-of-the-art explosion models.
