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/mT−−−√ 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 δf(x,p) which provides a better alternative to Grad's approximation for hydrodynamic modeling of relativistic heavy-ion collisions.
R. S. Bhalerao, Jaiswal, A., Pal, S., and V. Sreekanth, “Relativistic viscous hydrodynamics for heavy-ion collisions: A comparison between Chapman-Enskog and Grad’s methods”, Phys. Rev. C, vol. 89, p. 054903, 2014.