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

Abstract

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.

Authors:
 [1]; ORCiD logo [1];  [2]
  1. The Ohio State Univ., Columbus, OH (United States)
  2. Kent State Univ., Kent, OH (United States)
Publication Date:
Research Org.:
The Ohio State Univ., Columbus, OH (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP)
OSTI Identifier:
1604545
Alternate Identifier(s):
OSTI ID: 1179929
Grant/Contract Number:  
SC0004286; SC0004104
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review. C, Nuclear Physics
Additional Journal Information:
Journal Volume: 90; Journal Issue: 5; Journal ID: ISSN 0556-2813
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats

Bazow, Dennis, Heinz, Ulrich, and Strickland, Michael. Second-order (2+1) -dimensional anisotropic hydrodynamics. United States: N. p., 2014. Web. doi:10.1103/PhysRevC.90.054910.
Bazow, Dennis, Heinz, Ulrich, & Strickland, Michael. Second-order (2+1) -dimensional anisotropic hydrodynamics. United States. https://doi.org/10.1103/PhysRevC.90.054910
Bazow, Dennis, Heinz, Ulrich, and Strickland, Michael. Fri . "Second-order (2+1) -dimensional anisotropic hydrodynamics". United States. https://doi.org/10.1103/PhysRevC.90.054910. https://www.osti.gov/servlets/purl/1604545.
@article{osti_1604545,
title = {Second-order (2+1) -dimensional anisotropic hydrodynamics},
author = {Bazow, Dennis and Heinz, Ulrich and Strickland, Michael},
abstractNote = {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.},
doi = {10.1103/PhysRevC.90.054910},
url = {https://www.osti.gov/biblio/1604545}, journal = {Physical Review. C, Nuclear Physics},
issn = {0556-2813},
number = 5,
volume = 90,
place = {United States},
year = {2014},
month = {11}
}

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