Quadrature-based lattice Boltzmann model for relativistic flows

Abstract

Abstract. A quadrature-based finite-difference lattice Boltzmann model is developed that is suitable for simulating relativistic flows of massless particles. We briefly review the relativistc Boltzmann equation and present our model. The quadrature is constructed such that the stress-energy tensor is obtained as a second order moment of the distribution function. The results obtained with our model are presented for a particular instance of the Riemann problem (the Sod shock tube). We show that the model is able to accurately capture the behavior across the whole domain of relaxation times, from the hydrodynamic to the ballistic regime. The property of the model of being extendable to arbitrarily high orders is shown to be paramount for the recovery of the analytical result in the ballistic regime.

Relativistic lattice Boltzmann methods: Theory and applications

“…Higher orders would most probably require different strategies, e.g. off-lattice schemes, which drastically improve the spatial resolution of the grid, but have as drawbacks the need for interpolation and the introduction of artificial dissipation effects [43,47,77]; we do not consider these strategies in this paper.…”

Transport coefficients in ultrarelativistic kinetic theory

“…The authors of Refs. [20,23] note that employing the Chapman-Enskog value for η leads to better agreement with the BAMPS data than when the Grad value is employed.…”

“…The relativistic lattice Boltzmann (LB) method has also been used as a tool to solve the AWB equation [15][16][17][18][19][20][21][22][23][24]. The propagation of planar shock waves of massless [15,[17][18][19][20] and massive [22,23] particles was investigated using the LB method and the results were validated by comparison with the data obtained using the Boltzmann Approach to Multi Parton Scattering (BAMPS) reported in Refs. [25][26][27].…”

“…In order to compare the LB results obtained in the frame of the AWB equation and the BAMPS results, the shear viscosity to entropy ratio η/s must be kept constant. Matching within the LB method the values of η/s employed in the BAMPS simulations requires as an input the exact expression for the shear viscosity η, which can be obtained via Grad's 14 moment ap-proach [15,[17][18][19]22] or the Chapman-Enskog procedure [20,23]. The authors of Refs.…”

“…Next, a moment-based approach similar to the one introduced in Refs. [16,20,21,28] is considered, where the distribution function is expanded with respect to the Laguerre and Legendre polynomials, corresponding to the magnitude p of the particle momentum and the z component ξ = p z /p of its velocity, respectively. Retaining zeroth and first-order terms with respect to the Laguerre polynomials and terms up to second-order with respect to the Legendre polynomials, a system of 6 evolution equations is obtained for the density n, pressure P , velocity β, heat flux q, shear pressure Π and an extra nonhydrodynamic variable.…”