(3+1)D hydrodynamic simulation of relativistic heavy-ion collisions

TLDR

The Kurganov–Tadmor algorithm is a Riemann‑solver‑free, second‑order, high‑resolution scheme with very low numerical viscosity that handles shocks and discontinuities well. The authors present MUSIC, an implementation of this algorithm for relativistic 3+1‑dimensional fluid dynamics in heavy‑ion collision scenarios. MUSIC incorporates a lattice‑based equation of state, a three‑dimensional triangulation method for freeze‑out surface determination, and computes transverse‑momentum spectra, pseudorapidity distributions, and anisotropic flow coefficients v₂ and v₄ for Au+Au collisions at √s=200 GeV. The simulation yields high‑precision v₄ values that show little sensitivity to the initial condition or equation of state, while also providing v₂ and pseudorapidity‑dependent flow results.

Abstract

We present music, an implementation of the Kurganov-Tadmor algorithm for relativistic 3+1 dimensional fluid dynamics in heavy-ion collision scenarios. This Riemann-solver-free, second-order, high-resolution scheme is characterized by a very small numerical viscosity and its ability to treat shocks and discontinuities very well. We also incorporate a sophisticated algorithm for the determination of the freeze-out surface using a three dimensional triangulation of the hypersurface. Implementing a recent lattice based equation of state, we compute ${p}_{T}$-spectra and pseudorapidity distributions for Au+Au collisions at $\sqrt{s}=200 \mathrm{GeV}$ and present results for the anisotropic flow coefficients ${v}_{2}$ and ${v}_{4}$ as a function of both ${p}_{T}$ and pseudorapidity $\ensuremath{\eta}$. We were able to determine ${v}_{4}$ with high numerical precision, finding that it does not strongly depend on the choice of initial condition or equation of state.