Type Ia supernovae (SNe Ia) are important objects in astronomy and astrophysics. They are one of the brightest and common transients in the universe, a standard candle for a cosmic distance, and a dominant origin of iron group elements. It is widely accepted that SNe Ia are thermodynamical explosions of carbon-oxygen (CO) white dwarfs (WDs) in binary systems. Nevertheless, it is yet unclear what the companion stars are, and what the masses of the exploding CO WDs are. Recently, many sub-Chandrasekhar mass explosions in the double-degenerate scenario have been suggested. We have assessed the violent merger and Dynamically-Driven Double-Degenerate Double-Detonation (D 6) models by numerical simulations. We have concluded that the violent merger model may not explain normal SNe Ia, since their circum-binary matter is much larger than the size of SN 2011fe, and their event rate is much smaller than the SN Ia rate in our Galaxy by an order of magnitude. However, it can be progenitors of peculiar SNe Ia. The D 6 model has roughly consistent features with normal SNe Ia. However, the model has supernova ejecta with an asymmetric shape and low-velocity carbon-oxygen component due to the presence of the surviving companion CO. If these features can be observed, the D 6 model may be inconsistent with normal SNe Ia. In this case, the D 6 model can be also progenitors of peculiar SNe Ia.