Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of moment of the Boltzmann equation

TL;DR

This paper proposes a specific choice of moments of the Boltzmann equation to close the equations of anisotropic fluid dynamics, improving the match to Boltzmann solutions in boost-invariant expansion.

Contribution

It introduces a particular moment choice for closing anisotropic fluid dynamics equations, enhancing their accuracy in describing boost-invariant fluid expansion.

Findings

The chosen moment yields the best agreement with Boltzmann solutions.

The approach improves the predictive power of anisotropic fluid dynamics.

The method is tested in a one-dimensional boost-invariant setting.

Abstract

In Moln\'ar et al. [Phys. Rev. D 93, 114025 (2016)] the equations of anisotropic dissipative fluid dynamics were obtained from the moments of the Boltzmann equation based on an expansion around an arbitrary anisotropic single-particle distribution function. In this paper we make a particular choice for this distribution function and consider the boost-invariant expansion of a fluid in one dimension. In order to close the conservation equations, we need to choose an additional moment of the Boltzmann equation. We discuss the influence of the choice of this moment on the time evolution of fluid-dynamical variables and identify the moment that provides the best match of anisotropic fluid dynamics to the solution of the Boltzmann equation in the relaxation-time approximation.