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Relativistic viscous hydrodynamics for heavy-ion collisions: A comparison between the Chapman-Enskog and Grad methods

2014; American Institute of Physics; Volume: 89; Issue: 5 Linguagem: Inglês

10.1103/physrevc.89.054903

1538-4497

Rajeev S. Bhalerao, Amaresh Jaiswal, Subrata Pal, V. Sreekanth,

Quantum Chromodynamics and Particle Interactions

Derivations of relativistic second-order dissipative hydrodynamic equations have relied almost exclusively on the use of Grad's 14-moment approximation to write $f(x,p)$, the nonequilibrium distribution function in the phase space. Here we consider an alternative Chapman-Enskog-like method, which, unlike Grad's, involves a small expansion parameter. We derive an expression for $f(x,p)$ to second order in this parameter. We show analytically that while Grad's method leads to the violation of the experimentally observed $1/\sqrt{{m}_{T}}$ scaling of the longitudinal femtoscopic radii, the alternative method does not exhibit such an unphysical behavior. We compare numerical results for hadron transverse-momentum spectra and femtoscopic radii obtained in these two methods, within the one-dimensional scaling expansion scenario. Moreover, we demonstrate a rapid convergence of the Chapman-Enskog-like expansion up to second order. This leads to an expression for $\ensuremath{\delta}f(x,p)$ which provides a better alternative to Grad's approximation for hydrodynamic modeling of relativistic heavy-ion collisions.