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

TL;DR

THC is a high-order, high-resolution shock-capturing code designed for simulating both Newtonian and special-relativistic hydrodynamics, enabling detailed turbulence studies and benchmark tests.

Contribution

The paper introduces THC, a novel high-order flux-vector-splitting code with multiple reconstruction schemes, including a specialized WENO scheme for relativistic turbulence simulations.

Findings

Systematic comparison of reconstruction schemes in Newtonian and relativistic flows

Successful simulation of shock waves and Kelvin-Helmholtz instability

Demonstration of well-converged velocity spectra in turbulent flows

Abstract

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.