Derivation of anisotropic dissipative fluid dynamics from the Boltzmann equation

2016/02/29 by E. Molnár, E. Molnar, H. Niemi +2 · 87 citations
Mathematics · Physics and Astronomy · #Anisotropy #Boltzmann equation #Classical mechanics #Cosmology and Gravitation Theories #Dissipative system #Distribution function #Gas Dynamics and Kinetic Theory #High-Energy Particle Collisions Research #Isotropy #Mathematical physics #Momentum (technical analysis) #Physics #Quantum mechanics #Velocity Moments #hep-ph #nucl-th #physics.flu-dyn

paper · pdf · doi:10.1103/physrevd.93.114025

published in Physical review. D/Physical review. D. 93(11) (American Physical Society) · 52 pages; Abstract slightly changed; new references and new paragraph added

openalex publication_date 2016/06/22 · arxiv created 2016/06/23 · arxiv updated 2016/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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, \stackrel^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 from \stackrel^f_0k. Truncating this set via the 14-moment approximation, we obtain the equations of motion of anisotropic dissipative fluid dynamics.

Citations

• Boost-invariant (2+1)-dimensional anisotropic hydrodynamics
• Anisotropic hydrodynamics, bulk viscosities, andr-modes of strange quark stars with strong magnetic fields
• Highly anisotropic and strongly dissipative hydrodynamics for early stages of relativistic heavy-ion collisions
• Nonstationary irreversible thermodynamics: A causal relativistic theory
• Highly anisotropic and strongly dissipative hydrodynamics with transverse expansion
• Quasiparticle equation of state for anisotropic hydrodynamics
• The Thermodynamics of Irreversible Processes. III. Relativistic Theory of the Simple Fluid
• Dynamics and thermodynamics of complex fluids. I. Development of a general formalism

Cited by

• Exact solutions for the moments of the binary collision integral and its relation to the relaxation-time approximation in leading-order anisotropic fluid dynamics
• Viscous anisotropic hydrodynamics for the Gubser flow