Coupling Relativistic Viscous Hydrodynamics to Boltzmann Descriptions

TL;DR

This paper develops a method to seamlessly couple viscous hydrodynamics with Boltzmann models in relativistic heavy ion collision simulations, ensuring consistent stress-energy tensor continuity and providing a Monte Carlo sampling algorithm.

Contribution

It introduces a consistent coupling framework for viscous hydrodynamics and Boltzmann descriptions, including derivations for viscosity effects and a Monte Carlo sampling algorithm.

Findings

Derived viscosity expressions for gas phase

Reproduced non-equilibrium stress-energy tensor components

Presented a Monte Carlo sampling algorithm for particle initialization

Abstract

Models of relativistic heavy ion collisions typically involve both a hydrodynamic module to describe the high density liquid-like phase and a Boltzmann module to simulate the low density break-up phase which is gas-like. Coupling the prescriptions is more complicated for viscous prescriptions if one wants to maintain continuity of the entire stress-energy tensor and currents. Derivations for the viscosity for a gas are reviewed, which then lead to expressions for changes in the phase space occupation based on simple relaxation-time pictures of viscosity. These expressions are shown to consistently reproduce the non-equilibrium components of the stress-energy tensor. An algorithm for generating a Monte Carlo sampling of particles with which to initiate the Boltzmann calculations is also presented.