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

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.

38pages, 31 figures; published version

References in corpus (15)

• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• The QCD equation of state with dynamical quarks
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Elliptic and triangular flow in event-by-event (3+1)D viscous hydrodynamics
• 200 A GeV Au+Au collisions serve a nearly perfect quark-gluon liquid
• Space-time evolution of bulk QCD matter
• Effects of initial flow velocity fluctuation in event-by-event (3+1)D hydrodynamics
• Triangular flow in event-by-event ideal hydrodynamics in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=200A$ GeV
• Event-by-event hydrodynamics and elliptic flow from fluctuating initial state
• Elliptic flow in U+U collisions at sqrt{s_{NN}} = 200 GeV and in Pb+Pb collisions at sqrt{s_{NN}} = 2.76 TeV: Prediction from a hybrid approach
• Elliptic flow in Pb+Pb collisions at sqrt{s_{NN}} = 2.76 TeV: hybrid model assessment of the first data
• Exploring the Vacuum Geometry of N=1 Gauge Theories
• Stable First-order Particle-frame Relativistic Hydrodynamics for Dissipative Systems
• Kaon and pion femtoscopy at the highest energies available at the BNL Relativistic Heavy Ion Collider (RHIC) in a hydrokinetic model
• On the convexity of Relativistic Hydrodynamics

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• Solutions of Conformal Israel-Stewart Relativistic Viscous Fluid Dynamics
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• The iEBE-VISHNU code package for relativistic heavy-ion collisions
• A new relativistic viscous hydrodynamics code and its application to the Kelvin-Helmholtz instability in high-energy heavy-ion collisions
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• Constraining the equation of state with identified particle spectra
• Introduction to Hydrodynamics
• Temperature dependence of transport coefficients of QCD in high-energy heavy-ion collisions
• A new relativistic hydrodynamics code for high-energy heavy-ion collisions
• Radiative hadronization: Photon emission at hadronization from quark-gluon plasma
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