Lattice Boltzmann method for relativistic hydrodynamics: Issues on conservation law of particle number and discontinuities

Abstract

In this paper, we aim to address several important issues about the recently developed lattice Boltzmann (LB) model for relativistic hydrodynamics [M. Mendoza et al., Phys. Rev. Lett. 105, 014502 (2010); Phys. Rev. D 82, 105008 (2010)]. First, we study the conservation law of particle number in the relativistic LB model. Through the Chapman-Enskog analysis, it is shown that in the relativistic LB model the conservation equation of particle number is a convection-diffusion equation rather than a continuity equation, which makes the evolution of particle number dependent on the relaxation time. Furthermore, we investigate the origin of the discontinuities appeared in the relativistic problems with high viscosities, which were reported in a recent study [D. Hupp et al., Phys. Rev. D 84, 125015 (2011)]. A multiple-relaxation-time (MRT) relativistic LB model is presented to examine the influences of different relaxation times on the discontinuities. Numerical experiments show the discontinuities can be eliminated by setting the relaxation time ${\tau }_e$ (related to the bulk viscosity) to be sufficiently smaller than the relaxation time ${\tau }_v$ (related to the shear viscosity). Meanwhile, it is found that the relaxation time ${\tau }_{\epsilon }$, which has no effect on the conservation equations at the Navier-Stokes level, will affect the numerical accuracy of the relativistic LB model. Moreover, the accuracy of the relativistic LB model for simulating moderately relativistic problems is also investigated.

7 figures

References in corpus (14)

• Elliptic Flow of Identified Hadrons in Au+Au Collisions at sqrt(s_NN) = 200 GeV
• Relativistic Numerical Method for Close Neutron Star Binaries
• Lattice Boltzmann scheme for relativistic fluids
• Improved axisymmetric lattice Boltzmann scheme
• Lattice Boltzmann method for thermal flow simulation on standard lattices
• Transport rates and momentum isotropization of gluon matter in ultrarelativistic heavy-ion collisions
• Coupling lattice Boltzmann model for simulation of thermal flows on standard lattices
• Relativistic shock waves in viscous gluon matter
• Relativistic (Lattice) Boltzmann Equation with Non-Ideal Equation of State
• Multiple-Relaxation-Time Lattice Boltzmann Approach to Compressible Flows with Flexible Specific-Heat Ratio and Prandtl Number
• Investigation of shock waves in the relativistic Riemann problem: A comparison of viscous fluid dynamics to kinetic theory
• A fully relativistic lattice Boltzmann algorithm
• Derivation of the Lattice Boltzmann Model for Relativistic Hydrodynamics
• On the relativistic Lattice Boltzmann method for quark-gluon plasma simulations

Cited by in corpus (8)

• Relativistic Lattice Boltzmann Model with Improved Dissipation
• Relativistic Lattice Boltzmann Methods: Theory and Applications
• Lattice Boltzmann model for ultra-relativistic flows
• Towards a full solution of relativistic Boltzmann equation for quark-gluon matter on GPUs
• Towards a unified lattice kinetic scheme for relativistic hydrodynamics
• Fully dissipative relativistic lattice Boltzmann method in two dimensions
• Towards a Probabilistic Foundation of Relativistic Quantum Theory: The One-Body Born Rule in Curved Spacetime
• Multiple-relaxation-time lattice Boltzmann modeling of incompressible flows in porous media