Boost-Invariant (2+1)-dimensional Anisotropic Hydrodynamics

TL;DR

This paper applies anisotropic hydrodynamics to (2+1)-dimensional boost invariant systems, deriving equations from the Boltzmann equation, and solves them numerically to study collective flow under various initial conditions and viscosity parameters.

Contribution

It introduces a new framework for (2+1)-D boost invariant anisotropic hydrodynamics, including derivation of dynamical equations and development of two numerical methods for solutions.

Findings

Numerical solutions show the evolution of collective flow under different initial conditions.

The impact of shear viscosity to entropy ratio on flow development is quantified.

Two numerical schemes are validated for solving anisotropic hydrodynamics equations.

Abstract

We present results of the application of the anisotropic hydrodynamics (aHydro) framework to (2+1)-dimensional boost invariant systems. The necessary aHydro dynamical equations are derived by taking moments of the Boltzmann equation using a momentum-space anisotropic one-particle distribution function. We present a derivation of the necessary equations and then proceed to numerical solutions of the resulting partial differential equations using both realistic smooth Glauber initial conditions and fluctuating Monte-Carlo Glauber initial conditions. For this purpose we have developed two numerical implementations: one which is based on straightforward integration of the resulting partial differential equations supplemented by a two-dimensional weighted Lax-Friedrichs smoothing in the case of fluctuating initial conditions; and another that is based on the application of the Kurganov-Tadmor central scheme. For our final results we compute the collective flow of the matter via the lab-frame energy-momentum tensor eccentricity as a function of the assumed shear viscosity to entropy ratio, proper time, and impact parameter.