  The single-degenerate (SD) model is one of the leading models for the
progenitors of Type Ia supernovae (SNe Ia). Recently, a new version of the SD
model, the common-envelope wind (CEW) model, has been proposed, which, in
principle, has the potential to resolve most of the difficulties encountered by
previous SD models. This model is still being developed and a number of open
issues remain, such as the details of the mass-loss mechanism from the surface
of the common envelope (CE), the main observational properties, and the
spiral-in timescale of the binary inside the envelope. In this article, we aim
to address these issues by considering hydrodynamical effects on the CE. Using
the stellar evolution code MESA, we carried out a series of 1D hydrodynamical
simulations of an asymptotic giant branch (AGB) star undergoing a
common-envelope phase with different envelope masses (0.0007-0.06 solar mass).
We found that the envelopes are always dynamically unstable, leading to regular
mass ejection events if the envelope is more massive than the critical value of
~ 0.003 solar mass. The kappa mechanism can naturally explain this phenomenon.
We also found that, due to the low mass of the CE, the estimated frictional
luminosity caused by the spiral-in of the immersed binary is much less than the
nuclear luminosity, and therefore will not affect the structure of the CE
significantly. Our results imply that the CE in the CEW model cannot be very
massive. We also present a rough estimate for the spiral-in timescale based on
a simplified model. We found that, for reasonable assumptions, the timescale
may be longer than a few 100,000 yr; therefore, the white dwarf may have enough
time to increase its mass toward the Chandrasekhar mass, avoiding a merger with
the companion.
