Relativistic Lattice Boltzmann Model with Improved Dissipation

TL;DR

This paper introduces an improved relativistic lattice Boltzmann model that accurately captures dissipative effects in ultra-relativistic hydrodynamics, validated against full Boltzmann solutions and outperforming previous models.

Contribution

The authors develop a third order moment expansion of the Maxwell-Juettner distribution and incorporate a time dilatation to enhance dissipation modeling in relativistic LB schemes.

Findings

Excellent agreement with BAMPS simulations.

More accurate than previous relativistic LB models.

Validated for high viscosity and velocities.

Abstract

We develop a relativistic lattice Boltzmann (LB) model, providing a more accurate description of dissipative phenomena in relativistic hydrodynamics than previously available with existing LB schemes. The procedure applies to the ultra-relativistic regime, in which the kinetic energy (temperature) far exceeds the rest mass energy, although the extension to massive particles and/or low temperatures is conceptually straightforward. In order to improve the description of dissipative effects, the Maxwell-Juettner distribution is expanded in a basis of orthonormal polynomials, so as to correctly recover the third order moment of the distribution function. In addition, a time dilatation is also applied, in order to preserve the compatibility of the scheme with a cartesian cubic lattice. To the purpose of comparing the present LB model with previous ones, the time transformation is also applied to a lattice model which recovers terms up to second order, namely up to energy-momentum tensor. The approach is validated through quantitative comparison between the second and third order schemes with BAMPS (the solution of the full relativistic Boltzmann equation), for moderately high viscosity and velocities, and also with previous LB models in the literature. Excellent agreement with BAMPS and more accurate results than previous relativistic lattice Boltzmann models are reported.