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 ultrarelativistic 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-Juttner 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 the
energy-momentum tensor. The approach is validated through quantitative
comparison between the second- and third-order schemes with Boltzmann
approach multiparton scattering (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. DOI: 10.1103/PhysRevD.87.065027
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