  Vigorous mass loss in the classical Wolf-Rayet (WR) phase is important for
the late evolution and final fate of massive stars. We develop spherically
symmetric time-dependent and steady-state hydrodynamical models of the
radiation-driven wind outflows and associated mass loss from classical WR
stars. The simulations are based on combining the opacities typically used in
static stellar structure and evolution models with a simple parametrised form
for the enhanced line-opacity expected within a supersonic outflow. Our
simulations reveal high mass-loss rates initiated in deep and hot optically
thick layers around T\approx 200kK. The resulting velocity structure is
non-monotonic and can be separated into three phases: i) an initial
acceleration to supersonic speeds ii) stagnation and even deceleration, and
iii) an outer region of rapid re-acceleration. The characteristic structures
seen in converged steady-state simulations agree well with the outflow
properties of our time-dependent models. By directly comparing our dynamic
simulations to corresponding hydrostatic models, we demonstrate explicitly that
the need to invoke extra energy transport in convectively inefficient regions
of stellar structure and evolution models is merely an artefact of enforcing a
hydrostatic outer boundary. Moreover, the "dynamically inflated" inner regions
of our simulations provide a natural explanation for the often-found mismatch
between predicted hydrostatic WR radii and those inferred from spectroscopy.
Finally, we contrast our simulations with alternative recent WR wind models
based on co-moving frame radiative transfer for computing the radiation force.
Since CMF transfer currently cannot handle non-monotonic velocity fields, the
characteristic deceleration regions found here are avoided in such simulations
by invoking an ad-hoc very high degree of clumping.
