Two Dimensional Turbulence in a Massless Fluid with a Relativistic Lattice Boltzmann Model

TL;DR

This paper develops a relativistic lattice Boltzmann model to simulate two-dimensional turbulence in massless fluids, with potential applications to electron flows in novel materials like graphene.

Contribution

It introduces a relativistic extension of the lattice Boltzmann method specifically designed for turbulent, massless, 2D hydrodynamic systems, bridging classical and relativistic fluid simulations.

Findings

Successfully reproduces turbulence characteristics in a relativistic massless fluid

Demonstrates the model's potential for simulating electron flows in materials like graphene

Provides a quantitative tool for relativistic fluid dynamics in condensed matter physics

Abstract

We investigate a relativistic adaptation of the Lattice Boltzmann Method that reproduces the equations of motion for a turbulent, two-dimensional, massless hydrodynamic system. The classical Lattice Boltzmann Method and its extension to relativistic fluid dynamics is described. The numeric formulation is evaluated using a zero-averaged stirring force introduced into the numerics to induce turbulence, and the flow characteristics produced are compared to properties of a classical turbulent hydrodynamic flow. The model can reasonably be expected to offer quantitative simulations of electron fluid flows in graphene or Kagome lattices.