  A grid of numerical simulations of double-diffusive convection is presented
for the astrophysical case where viscosity (Prandtl number Pr) and solute
diffusivity (Lewis number Le) are much smaller than the thermal diffusivity. As
in laboratory and geophysical cases convection takes place in a layered form.
The proper translation between subsonic flows in a stellar interior and an
incompressible (Boussinesq) fluid is given, and the validity of the Boussinesq
approximation for the semiconvection problem is checked by comparison with
fully compressible simulations. The predictions of a simplified theory of
mixing in semiconvection given in a companion paper are tested against the
numerical results, and used to extrapolate these to astrophysical conditions.
The predicted effective He-diffusion coefficient is nearly independent of the
double-diffusive layering thickness $d$. For a fiducial main sequence model (15
$M_\odot$) the inferred mixing time scale is of the order $10^{10}$ yr. An
estimate for the secular increase of $d$ during the semiconvective phase is
given. It can potentially reach a significant fraction of a pressure scale
height.
