A new scheme of causal viscous hydrodynamics for relativistic heavy-ion collisions: A Riemann solver for quark-gluon plasma

TL;DR

This paper introduces a high-precision numerical algorithm based on the second-order Godunov method for solving relativistic viscous hydrodynamics equations with QCD equations of state, crucial for modeling quark-gluon plasma in heavy-ion collisions.

Contribution

It presents a novel, less dissipative numerical scheme with an explicit expression for numerical viscosity, enhancing accuracy in simulating quark-gluon plasma dynamics.

Findings

The algorithm accurately models sound wave propagation and shock phenomena.

Explicit numerical viscosity expression helps optimize cell size for physical viscosity effects.

Validated through multiple numerical test problems.

Abstract

In this article, we present a state-of-the-art algorithm for solving the relativistic viscous hydrodynamics equation with the QCD equation of state. The numerical method is based on the second-order Godunov method and has less numerical dissipation, which is crucial in describing of quark-gluon plasma in high-energy heavy-ion collisions. We apply the algorithm to several numerical test problems such as sound wave propagation, shock tube and blast wave problems. In sound wave propagation, the intrinsic numerical viscosity is measured and its explicit expression is shown, which is the second-order of spatial resolution both in the presence and absence of physical viscosity. The expression of the numerical viscosity can be used to determine the maximum cell size in order to accurately measure the effect of physical viscosity in the numerical simulation.