  We carry out non-rotating high-resolution calculations of the solar global
convection, which resolve convective scales of less than 10 Mm. To cope with
the low Mach number conditions in the lower convection zone, we use the reduced
speed of sound technique (RSST), which is simple to implement and requires only
local communication in the parallel computation. In addition, the RSST allows
us to expand the computational domain upward to about $0.99 R_{\odot}$ as it
can also handle compressible flows. Using this approach, we study the solar
convection zone on the global scale, including small-scale near-surface
convection. In particular, we investigate the influence of the top boundary
condition on the convective structure throughout the convection zone as well as
on small-scale dynamo action. Our main conclusions are: 1. The small-scale
downflows generated in the near-surface layer penetrate into deeper layers to
some extent and excite small-scale turbulence in the region $>0.9R_\odot$,
where $R_\odot$ is the solar radius. 2. In the deeper convection zone
($<0.9R_\odot$), the convection is not influenced by the location of the upper
boundary. 3. Using an LES approach, we can achieve small-scale dynamo action
and maintain a field of about $0.15-0.25 B_\mathrm{eq}$ throughout the
convection zone, where $B_\mathrm{eq}$ is the equipartition magnetic field to
the kinetic energy. 4. The overall dynamo efficiency varies significantly in
the convection zone as a consequence of the downward directed Poynting flux and
the depth variation of the intrinsic convective scales.
