  We present THC: a new high-order flux-vector-splitting code for Newtonian and
special-relativistic hydrodynamics designed for direct numerical simulations of
turbulent flows. Our code implements a variety of different reconstruction
algorithms, such as the popular weighted essentially non oscillatory and
monotonicity-preserving schemes, or the more specialised bandwidth-optimised
WENO scheme that has been specifically designed for the study of compressible
turbulence. We show the first systematic comparison of these schemes in
Newtonian physics as well as for special-relativistic flows. In particular we
will present the results obtained in simulations of grid-aligned and oblique
shock waves and nonlinear, large-amplitude, smooth adiabatic waves. We will
also discuss the results obtained in classical benchmarks such as the
double-Mach shock reflection test in Newtonian physics or the linear and
nonlinear development of the relativistic Kelvin-Helmholtz instability in two
and three dimensions. Finally, we study the turbulent flow induced by the
Kelvin-Helmholtz instability and we show that our code is able to obtain
well-converged velocity spectra, from which we benchmark the effective
resolution of the different schemes.
