Second-order (2+1) -dimensional anisotropic hydrodynamics

Bazow, Dennis; Heinz, Ulrich; Strickland, Michael

doi:10.1103/PhysRevC.90.054910

Second-order $(2 + 1)$ -dimensional anisotropic hydrodynamics

Journal Article · Fri Nov 21 00:00:00 EST 2014 · Physical Review C, Nuclear Physics

DOI:https://doi.org/10.1103/PhysRevC.90.054910· OSTI ID:1604545

Bazow, Dennis ^[1]; ^[2]; Strickland, Michael ^[3]

The Ohio State Univ., Columbus, OH (United States); The Ohio State University
The Ohio State Univ., Columbus, OH (United States)
Kent State Univ., Kent, OH (United States)

We present a complete formulation of second-order (2+1)-dimensional anisotropic hydrodynamics. The resulting framework generalizes leading-order anisotropic hydrodynamics by allowing for deviations of the one-particle distribution function from the spheroidal form assumed at leading order. We derive complete second-order equations of motion for the additional terms in the macroscopic currents generated by these deviations from their kinetic definition using a Grad-Israel-Stewart 14-moment ansatz. The result is a set of coupled partial differential equations for the momentum-space anisotropy parameter, effective temperature, the transverse components of the fluid four-velocity, and the viscous tensor components generated by deviations of the distribution from spheroidal form. We then perform a quantitative test of our approach by applying it to the case of one-dimensional boost-invariant expansion in the relaxation time approximation (RTA) in which case it is possible to numerically solve the Boltzmann equation exactly.We demonstrate that the second-order anisotropic hydrodynamics approach provides an excellent approximation to the exact (0+1)-dimensional RTA solution for both small and large values of the shear viscosity.

View Accepted Manuscript (DOE)

Research Organization:: The Ohio State Univ., Columbus, OH (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

Grant/Contract Number:: SC0004104; SC0004286

OSTI ID:: 1604545

Alternate ID(s):: OSTI ID: 1179929

Journal Information:: Physical Review C, Nuclear Physics, Journal Name: Physical Review C, Nuclear Physics Journal Issue: 5 Vol. 90; ISSN 0556-2813; ISSN PRVCAN

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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