High-order quadrature-based lattice Boltzmann models for the flow of ultrarelativistic rarefied gases
arXiv:1612.01287 · doi:10.1103/PhysRevC.98.035201
Abstract
We present a systematic procedure for the construction of relativistic lattice Boltzmann models (R-SLB) appropriate for the simulation of flows of massless particles. Quadrature rules are used for the discretization of the momentum space in spherical coordinates. The models are optimized for one-dimensional flows. The applications considered in this paper are the Sod shock tube and the one-dimensional boost invariant expansion (Bjorken flow). Our models are tested against exact solutions in the inviscid and ballistic limits. At intermediate relaxation times (finite viscosity), we compare with the results obtained using the Boltzmann approach of multiparton scattering model for the Sod shock tube problem, as well as with a semi-analytic solution for the non-ideal Bjorken flow. In all cases our models give remarkably good results. We define a convergence test in order to find the quadrature order necessary to obtain convergence at a predefined accuracy. We show that, while in the hydrodynamic regime the number of velocities is comparable to that required for the more popular collision-streaming type models, as we go towards the ballistic regime, the size of the velocity set must be substantially increased in order to accurately reproduce the analytic profiles.
arXiv comment43 pages (double column), 16 figures, 4 tables
References in corpus (93)
- Experimental and Theoretical Challenges in the Search for the Quark Gluon Plasma: The STAR Collaboration's Critical Assessment of the Evidence from RHIC Collisions
- Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration
- Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
- Quark Gluon Plasma an Color Glass Condensate at RHIC? The perspective from the BRAHMS experiment
- A Stress Tensor for Anti-de Sitter Gravity
- Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma
- Evolution of Binary Black Hole Spacetimes
- Collective flow and viscosity in relativistic heavy-ion collisions
- New Forms of QCD Matter Discovered at RHIC
- Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
- Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium
- The QCD transition temperature: results with physical masses in the continuum limit
- Energy loss of a heavy quark moving through N=4 supersymmetric Yang-Mills plasma
- Quasinormal modes and holography
- Derivation of transient relativistic fluid dynamics from the Boltzmann equation
- Bottom-up thermalization in heavy ion collisions
- Entropy and Temperature of Black 3-Branes
- New Developments in Relativistic Viscous Hydrodynamics
- Calculating the Jet Quenching Parameter from AdS/CFT
- Distributions of Charged Hadrons Associated with High Transverse Momentum Particles in pp and Au+Au Collisions at sqrt(s_NN)=200 GeV
- Measurement of the azimuthal anisotropy for charged particle production in sqrt(s_NN) = 2.76 TeV lead-lead collisions with the ATLAS detector
- Collective Modes of an Anisotropic Quark-Gluon Plasma
- Classical Black Hole Production in High-Energy Collisions
- A calculation of the bulk viscosity in SU(3) gluodynamics
- A calculation of the shear viscosity in SU(3) gluodynamics
- The importance of the bulk viscosity of QCD in ultrarelativistic heavy-ion collisions
- Scaling properties of azimuthal anisotropy in Au+Au and Cu+Cu collisions at sqrt(s_NN) = 200 GeV
- Measurements of Higher-Order Flow Harmonics in Au+Au Collisions at sqrt(s_NN) = 200 GeV
- Early thermalization at RHIC
- Supersymmetric Gauge Theories and the AdS/CFT Correspondence
- Discrete unified gas kinetic scheme for all Knudsen number flows: II. Compressible case
- Brane World Cosmology - Gauge-Invariant Formalism for Perturbation
- Hydrodynamics of R-charged black holes
- Symmetry constraints on generalizations of Bjorken flow
- An AdS/CFT Calculation of Screening in a Hot Wind
- Apparent Thermalization due to Plasma Instabilities in Quark-Gluon Plasma
- Quasinormal frequencies of Schwarzschild black holes in anti-de Sitter spacetimes: A complete study on the asymptotic behavior
- Holographic melting and related properties of mesons in a quark gluon plasma
- Transport Properties of the Quark-Gluon Plasma -- A Lattice QCD Perspective
- Testing viscous and anisotropic hydrodynamics in an exactly solvable case
- Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
- Black Holes, Shock Waves, and Causality in the AdS/CFT Correspondence
- Measurement of higher-order harmonic azimuthal anisotropy in PbPb collisions at a nucleon-nucleon center-of-mass energy of 2.76 TeV
- Gauge/gravity duality and thermalization of a boost-invariant perfect fluid
- Relativistic third-order dissipative fluid dynamics from kinetic theory
- Third-order relativistic dissipative hydrodynamics
- Lattice Boltzmann scheme for relativistic fluids
- Relativistic dissipative hydrodynamics from kinetic theory with relaxation time approximation
- A Holographic Dual of Hydrodynamics
- A Gravity Dual of RHIC Collisions
- Expanding plasmas and quasinormal modes of anti-de Sitter black holes
- Transport coefficients for bulk viscous evolution in the relaxation time approximation
- Relativistic hydrodynamics in heavy-ion collisions: general aspects and recent developments
- The stress tensor of a quark moving through N=4 thermal plasma
- Thermal spectral functions of strongly coupled N=4 supersymmetric Yang-Mills theory
- Finite difference lattice Boltzmann model with flux limiters for liquid-vapor systems
- Relativistic shock waves in viscous gluon matter
- Relativistic (Lattice) Boltzmann Equation with Non-Ideal Equation of State
- Spectra and elliptic flow for identified hadrons in 2.76 A TeV Pb+Pb collisions
- Investigation of shock waves in the relativistic Riemann problem: A comparison of viscous fluid dynamics to kinetic theory
- Lattice Boltzmann study on Kelvin-Helmholtz instability: the roles of velocity and density gradients
- A fully relativistic lattice Boltzmann algorithm
- Transport properties of the quark-gluon plasma from lattice QCD
- Relativistic second-order dissipative hydrodynamics at finite chemical potential
- Relativistic quantum transport coefficients for second-order viscous hydrodynamics
- Hydrodynamic Model for Conductivity in Graphene
- Relativistic viscous hydrodynamics for heavy-ion collisions: A comparison between the Chapman-Enskog and Grad methods
- Complete relativistic second-order dissipative hydrodynamics from the entropy principle
- Conservative 3+1 General Relativistic Boltzmann Equation
- Relativistic Lattice Boltzmann Model with Improved Dissipation
- Perturbative calculation of quasi-normal modes of AdS Schwarzschild black holes
- New relativistic dissipative fluid dynamics from kinetic theory
- Lattice Boltzmann model for ultra-relativistic flows
- Kinetic approach to relativistic dissipation
- Development of relativistic shock waves in viscous gluon matter
- On the relativistic Lattice Boltzmann method for quark-gluon plasma simulations
- Kelvin-Helmholtz instability of the Dirac fluid of charge carriers on graphene
- Towards a unified lattice kinetic scheme for relativistic hydrodynamics
- Maxwell-Juttner distribution for rigidly-rotating flows in spherically symmetric spacetimes using the tetrad formalism
- Modelling the influence of photospheric turbulence on solar flare statistics
- Study of transport coefficients in ultrarelativistic kinetic theory
- Relaxation-time approximation and relativistic third-order viscous hydrodynamics from kinetic theory
- Shell-like Structures in an expanding Quark-Antiquark Plasma
- Perfect fluidity of a dissipative system: Analytical solution for the Boltzmann equation in
- Boltzmann equation with a nonlocal collision term and the resultant dissipative fluid dynamics
- A new relativistic hydrodynamics code for high-energy heavy-ion collisions
- Relativistic rotating Boltzmann gas using the tetrad formalism
- Implementation of the force term in half-range lattice Boltzmann models
- Anderson-Witting transport coefficients for flows in general relativity
- Quadrature-based Lattice Boltzmann Model for Relativistic Flows
- The Milne spacetime and the hadronic Rindler horizon
- Transport coefficients in second-order non-conformal viscous hydrodynamics
- Quark-Gluon Plasma Thermalization and Plasma Instabilities
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- Dissipative hydrodynamics of relativistic shock waves in a Quark Gluon Plasma: comparing and benchmarking alternate numerical methods
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- A Lattice Boltzmann Method for Relativistic Rarefied Flows in (2 + 1) Dimensions
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- Hydrodynamic description of the baryon-charged quark-gluon plasma
- Bounded flows of dense gases
- Shakhov-type extension of the relaxation time approximation in relativistic kinetic theory and second-order fluid dynamics
- Lattice Boltzmann method for warm fluid simulations of plasma wakefield acceleration
- Bjorken flow revisited: analytic and numerical solutions in flat space-time coordinates
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- Realizability conditions for relativistic gases with a non-zero heat flux
- Lattice Boltzmann study of the one-dimensional boost-invariant expansion with anisotropic initial conditions
- Two Dimensional Turbulence in a Massless Fluid with a Relativistic Lattice Boltzmann Model