Boost-Invariant (2+1)-Dimensional Anisotropic Hydrodynamics

We present results of the application of the anisotropic hydrodynamics (aHydro) framework to (2+1)dimensional boost-invariant systems. The necessary aHydro dynamical equations are derived by taking moments of the Boltzmann equation using a momentum-space anisotropic one-particle distribution function. We present a derivation of the necessary equations and then proceed to numerical solutions of the resulting partial differential equations using both realistic smooth Glauber initial conditions and fluctuating Monte Carlo Glauber initial conditions. For this purpose we have developed two numerical implementations: one that is based on straightforward integration of the resulting partial differential equations supplemented by a two-dimensional weighted Lax-Friedrichs smoothing in the case of fluctuating initial conditions and another that is based on the application of the Kurganov-Tadmor central scheme. For our final results we compute the collective flow of the matter via the laboratory-frame energy-momentum tensor eccentricity as a function of the assumed shear viscosity-to-entropy ratio, proper time, and impact parameter. Required Publisher's Statement Original version available from publisher at: http://prc.aps.org/pdf/PRC/v85/i6/e064913 This article is available at The Cupola: Scholarship at Gettysburg College: http://cupola.gettysburg.edu/physfac/60 PHYSICAL REVIEW C 85, 064913 (2012) Boost-invariant (2+ 1)-dimensional anisotropic hydrodynamics Mauricio Martinez,1 Radoslaw Ryblewski,2 and Michael Strickland3,4 1Departamento de Fı́sica de Partı́culas, Universidade de Santiago de Compostela, Santiago de Compostela, E-15782 Galicia, Spain 2The H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, PL-31342 Kraków, Poland 3Physics Department, Gettysburg College, Gettysburg, Pennsylvania 17325, USA 4Frankfurt Institute for Advanced Studies, D-60438 Frankfurt am Main, Germany (Received 13 April 2012; published 19 June 2012) We present results of the application of the anisotropic hydrodynamics (aHydro) framework to (2+ 1)dimensional boost-invariant systems. The necessary aHydro dynamical equations are derived by taking moments of the Boltzmann equation using a momentum-space anisotropic one-particle distribution function. We present a derivation of the necessary equations and then proceed to numerical solutions of the resulting partial differential equations using both realistic smooth Glauber initial conditions and fluctuating Monte Carlo Glauber initial conditions. For this purpose we have developed two numerical implementations: one that is based on straightforward integration of the resulting partial differential equations supplemented by a two-dimensional weighted Lax-Friedrichs smoothing in the case of fluctuating initial conditions and another that is based on the application of the Kurganov-Tadmor central scheme. For our final results we compute the collective flow of the matter via the laboratory-frame energy-momentum tensor eccentricity as a function of the assumed shear viscosity-to-entropy ratio, proper time, and impact parameter. DOI: 10.1103/PhysRevC.85.064913 PACS number(s): 12.38.Mh, 24.10.Nz, 25.75.Ld, 47.75.+f