From kinetic theory to dissipative fluid dynamics

Betz, Barbara; Henkel, Danielle M.; Rischke, Dirk H.

doi:10.1016/j.ppnp.2008.12.018

Cited by 73 publications

(72 citation statements)

References 27 publications

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“…Similar approaches have been pursued in Refs. [14][15][16]. Recently, following the original idea of Grad [17], the deviation δf k has been expanded in a set of orthogonal polynomials in energy, E ku = k µ u µ , and irreducible tensors in momentum, 1, k µ , k µ k ν , .…”

Section: Introductionmentioning

confidence: 99%

Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation

2016

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Fluid-dynamical equations of motion can be derived from the Boltzmann equation in terms of an expansion around a single-particle distribution function which is in local thermodynamical equilibrium, i.e., isotropic in momentum space in the rest frame of a fluid element. However, in situations where the single-particle distribution function is highly anisotropic in momentum space, such as the initial stage of heavy-ion collisions at relativistic energies, such an expansion is bound to break down. Nevertheless, one can still derive a fluid-dynamical theory, called anisotropic dissipative fluid dynamics, in terms of an expansion around a single-particle distribution function,f 0k , which incorporates (at least parts of) the momentum anisotropy via a suitable parametrization. We construct such an expansion in terms of polynomials in energy and momentum in the direction of the anisotropy and of irreducible tensors in the two-dimensional momentum subspace orthogonal to both the fluid velocity and the direction of the anisotropy. From the Boltzmann equation we then derive the set of equations of motion for the irreducible moments of the deviation of the single-particle distribution function fromf 0k . Truncating this set via the 14-moment approximation, we obtain the equations of motion of anisotropic dissipative fluid dynamics.

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Section: Introductionmentioning

confidence: 99%

Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation

2016

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“…In recent years, relativistic dissipative fluid dynamics based on the IS formulation was extensively applied to describe the dynamics of nuclear collisions. At the same time, the theoretical foundations of this theory were further explored both from kinetic theory [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] and from irreversible thermodynamics [41][42][43][44][45][46][47][48][49][50][51]. In particular, in Refs.…”

Section: Introduction and Conclusionmentioning

confidence: 99%

Relative importance of second-order terms in relativistic dissipative fluid dynamics

et al. 2014

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In Denicol et al. [Phys. Rev. D 85, 114047 (2012)], the equations of motion of relativistic dissipative fluid dynamics were derived from the relativistic Boltzmann equation. These equations contain a multitude of terms of second order in the Knudsen number, in the inverse Reynolds number, or their product. Terms of second order in the Knudsen number give rise to nonhyperbolic (and thus acausal) behavior and must be neglected in (numerical) solutions of relativistic dissipative fluid dynamics. The coefficients of the terms which are of the order of the product of Knudsen and inverse Reynolds numbers have been explicitly computed in the above reference, in the limit of a massless Boltzmann gas. Terms of second order in the inverse Reynolds number arise from the collision term in the Boltzmann equation, upon expansion to second order in deviations from the single-particle distribution function in local thermodynamical equilibrium. In this work, we compute these second-order terms for a massless Boltzmann gas with constant scattering cross section. Consequently, we assess their relative importance in comparison to the terms which are of the order of the product of the Knudsen and inverse Reynolds numbers.

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“…Therein, the equations of (for many EoS) causal Israel-Stewart theory [39,40] are solved. Recently, however, corrections to this second order in gradients theory were reported [41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Shear and bulk viscosities of the gluon plasma in a quasiparticle description

2011

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Shear and bulk viscosities of deconfined gluonic matter are investigated within an effective kinetic theory by describing the strongly interacting medium phenomenologically in terms of quasiparticle excitations with medium-dependent self-energies. We show that the resulting transport coefficients reproduce the parametric dependencies on temperature and coupling obtained in perturbative QCD at large temperatures and small running coupling. The extrapolation into the nonperturbative regime results in a decreasing specific shear viscosity with decreasing temperature, exhibiting a minimum in the vicinity of the deconfinement transition, while the specific bulk viscosity is sizable in this region, falling off rapidly with increasing temperature. The temperature dependence of specific shear and bulk viscosities found within this quasiparticle description of the pure gluon plasma is in agreement with available lattice QCD results.

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From kinetic theory to dissipative fluid dynamics

Cited by 73 publications

References 27 publications

Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation

Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation

Relative importance of second-order terms in relativistic dissipative fluid dynamics

Shear and bulk viscosities of the gluon plasma in a quasiparticle description

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