Testing different formulations of leading-order anisotropic hydrodynamics

TL;DR

This paper evaluates a new set of leading-order anisotropic hydrodynamics equations against exact Boltzmann solutions, demonstrating improved accuracy over traditional viscous hydrodynamics in modeling pressure anisotropy.

Contribution

The paper introduces and tests a new formulation of leading-order anisotropic hydrodynamics, showing its superior performance in reproducing exact solutions compared to previous models.

Findings

New anisotropic hydrodynamics equations agree well with exact solutions.

Better reproduction of pressure anisotropy than second-order viscous hydrodynamics.

Transport coefficients align with second-order viscous hydrodynamics results.

Abstract

A recently obtained set of the equations for leading-order (3+1)D anisotropic hydrodynamics is tested against exact solutions of the Boltzmann equation with the collisional kernel treated in the relaxation time approximation. In order to perform the detailed comparisons, the new anisotropic hydrodynamics equations are reduced to the boost-invariant and transversally homogeneous case. The agreement with the exact solutions found using the new anisotropic hydrodynamics equations is similar to that found using previous, less general, formulations of anisotropic hydrodynamics. In addition, we find that, when compared to a state-of-the-art second-order viscous hydrodynamics framework, leading-order anisotropic hydrodynamics better reproduces the exact solution for the pressure anisotropy and gives comparable results for the bulk pressure evolution. Finally, we compare the transport coefficients obtained using linearized anisotropic hydrodynamics with results obtained using second-order viscous hydrodynamics.