High-order Shakhov-like extension of the relaxation time approximation in relativistic kinetic theory

Abstract

In this paper we present a relativistic Shakhov-type generalization of the Anderson-Witting relaxation time model for the Boltzmann collision integral. The extension is performed by modifying the path on which the distribution function $f_{\mathbf{k}}$ is taken towards local equilibrium $f_{0\mathbf{k}}$, by replacing $f_{\mathbf{k}}-f_{0\mathbf{k}}$ via $f_{\mathbf{k}}-f_{\mathrm{S}\mathbf{k}}$. The Shakhov-like distribution $f_{\mathrm{S}\mathbf{k}}$ is constructed using $f_{0\mathbf{k}}$ and the irreducible moments ${\rho }_r^{{\mu }_1\cdots {\mu }_{\ell }}$ of $f_{\mathbf{k}}$ and reduces to $f_{0\mathbf{k}}$ in local equilibrium. Employing the method of moments, we derive systematic high-order Shakhov extensions that allow both the first- and the second-order transport coefficients to be controlled independently of each other. We illustrate the capabilities of the formalism by tweaking the shear-bulk coupling coefficient ${\lambda }_{\Pi \pi }$ in the frame of the Bjorken flow of massive particles, as well as the diffusion-shear transport coefficients ${\ell }_{V\pi }$, ${\ell }_{\pi V}$ in the frame of sound wave propagation in an ultrarelativistic gas. Finally, we illustrate the importance of second-order transport coefficients by comparison with the results of the stochastic BAMPS method in the context of the one-dimensional Riemann problem.

arXiv comment38 pages, 8 figures, 2 tables

References in corpus (31)

• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade
• Testing viscous and anisotropic hydrodynamics in an exactly solvable case
• A new exact solution of the relativistic Boltzmann equation and its hydrodynamic limit
• Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation
• Relativistic shock waves in viscous gluon matter
• Hydrodynamic attractors, initial state energy and particle production in relativistic nuclear collisions
• On the relative importance of second-order terms in relativistic dissipative fluid dynamics
• Exact solution of the (0+1)-dimensional Boltzmann equation for a massive gas
• Flow in AA and pA as an interplay of fluid-like and non-fluid like excitations
• Investigation of shock waves in the relativistic Riemann problem: A comparison of viscous fluid dynamics to kinetic theory
• A fully relativistic lattice Boltzmann algorithm
• Analytic solution of the Boltzmann equation in an expanding system
• Opacity dependence of elliptic flow in kinetic theory
• Multicomponent relativistic dissipative fluid dynamics from the Boltzmann equation
• Relativistic Lattice Boltzmann Methods: Theory and Applications
• Establishing the Range of Applicability of Hydrodynamics in High-Energy Collisions
• Development of transverse flow at small and large opacities in conformal kinetic theory
• Inverse-Reynolds-Dominance approach to transient fluid dynamics
• High-order quadrature-based lattice Boltzmann models for the flow of ultrarelativistic rarefied gases
• Global flow structure and exact formal transseries of the Gubser flow in kinetic theory
• Hydrodynamic theories for a system of weakly self-interacting classical ultra-relativistic scalar particles: microscopic derivations and attractors
• Is Relativistic Hydrodynamics always Symmetric-Hyperbolic in the Linear Regime?
• Opacity dependence of transverse flow, pre-equilibrium and applicability of hydrodynamics in heavy-ion collisions
• Transport coefficients of second-order relativistic fluid dynamics in the relaxation-time approximation
• Study of transport coefficients in ultrarelativistic kinetic theory
• Fast kinetic simulator for relativistic matter
• Analytical structure of the binary collision integral and the ultrarelativistic limit of transport coefficients of an ideal gas
• Relativistic second-order dissipative and anisotropic fluid dynamics in the relaxation-time approximation for an ideal gas of massive particles
• Quadrature-based Lattice Boltzmann model for non-equilibrium dense gas flows
• Shakhov-type extension of the relaxation time approximation in relativistic kinetic theory and second-order fluid dynamics

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