Relativistic Lattice Boltzmann Model with Improved Dissipation

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.

12 pages, 5 figures

References in corpus (4)

• Electric Field Effect in Atomically Thin Carbon Films
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Derivation of the Lattice Boltzmann Model for Relativistic Hydrodynamics
• Lattice Boltzmann method for relativistic hydrodynamics: Issues on conservation law of particle number and discontinuities

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