  In the "double-detonation sub-Chandrasekhar" model for type Ia supernovae, a
carbon-oxygen (C + O) white dwarf accumulates sufficient amounts of helium such
that a detonation ignites in that layer before the Chandrasekhar mass is
reached. This detonation is thought to trigger a secondary detonation in the C
+ O core. By means of one- and two-dimensional hydrodynamic simulations, we
investigate the robustness of this explosion mechanism for generic 1-M_sun
models and analyze its observable predictions. Also a resolution dependence in
numerical simulations is analyzed. The propagation of thermonuclear detonation
fronts, both in helium and in the carbon-oxygen mixture, is computed by means
of both a level-set function and a simplified description for nuclear
reactions. The decision whether a secondary detonation is triggered in the
white dwarf's core or not is made based on criteria given in the literature. In
a parameter study involving different initial flame geometries for He-shell
masses of 0.2 and 0.1 M_sun, we find that a secondary detonation ignition is a
very robust process. Converging shock waves originating from the detonation in
the He shell generate the conditions for a detonation near the center of the
white dwarf in most of the cases considered. Finally, we follow the complete
evolution of three selected models with 0.2 M_sun of He through the
C/O-detonation phase and obtain nickel-masses of about 0.40 to 0.45 M_sun.
Although we have not done a complete scan of the possible parameter space, our
results show that sub-Chandrasekhar models are not good candidates for normal
or sub-luminous type Ia supernovae. The chemical composition of the ejecta
features significant amounts of nickel in the outer layers at high expansion
velocities, which is inconsistent with near-maximum spectra. (abbreviated)
