  (Abridged) In the implicit large eddy simulation (ILES) paradigm, the
dissipative nature of high-resolution shock-capturing schemes is exploited to
provide an implicit model of turbulence. Recent 3D simulations suggest that
turbulence might play a crucial role in core-collapse supernova explosions,
however the fidelity with which turbulence is simulated in these studies is
unclear. Especially considering that the accuracy of ILES for the regime of
interest in CCSN, weakly compressible and strongly anisotropic, has not been
systematically assessed before. In this paper we assess the accuracy of ILES
using numerical methods most commonly employed in computational astrophysics by
means of a number of local simulations of driven, weakly compressible,
anisotropic turbulence. We report a detailed analysis of the way in which the
turbulent cascade is influenced by the numerics. Our results suggest that
anisotropy and compressibility in CCSN turbulence have little effect on the
turbulent kinetic energy spectrum and a Kolmogorov $k^{-5/3}$ scaling is
obtained in the inertial range. We find that, on the one hand, the kinetic
energy dissipation rate at large scales is correctly captured even at
relatively low resolutions, suggesting that very high effective Reynolds number
can be achieved at the largest scales of the simulation. On the other hand, the
dynamics at intermediate scales appears to be completely dominated by the
so-called bottleneck effect, \ie the pile up of kinetic energy close to the
dissipation range due to the partial suppression of the energy cascade by
numerical viscosity. An inertial range is not recovered until the point where
relatively high resolution $\sim 512^3$, which would be difficult to realize in
global simulations, is reached. We discuss the consequences for CCSN
simulations.
