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We present THC: a new high-order flux-vector-splitting code for Newtonian andspecial-relativistic hydrodynamics designed for direct numerical simulations ofturbulent flows. Our code implements a variety of different reconstructionalgorithms, such as the popular weighted essentially non oscillatory andmonotonicity-preserving schemes, or the more specialised bandwidth-optimisedWENO scheme that has been specifically designed for the study of compressibleturbulence. We show the first systematic comparison of these schemes inNewtonian physics as well as for special-relativistic flows. In particular wewill present the results obtained in simulations of grid-aligned and obliqueshock waves and nonlinear, large-amplitude, smooth adiabatic waves. We willalso discuss the results obtained in classical benchmarks such as thedouble-Mach shock reflection test in Newtonian physics or the linear andnonlinear development of the relativistic Kelvin-Helmholtz instability in twoand three dimensions. Finally, we study the turbulent flow induced by theKelvin-Helmholtz instability and we show that our code is able to obtainwell-converged velocity spectra, from which we benchmark the effectiveresolution of the different schemes.

THC: a new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics