Elliptic flow in transport theory and hydrodynamics

Abstract

We present a new direct simulation Monte-Carlo method for solving the relativistic Boltzmann equation. We solve numerically the 2-dimensional Boltzmann equation using this new algorithm. We find that elliptic flow from this transport calculation smoothly converges towards the value from ideal hydrodynamics as the number of collisions per particle increases, as expected on general theoretical grounds, but in contrast with previous transport calculations.

Figures (3)

• Figure 1: Picture of a collision between a particle 1 of size $\sigma_{2d}=2 r$ and a pointlike particle $2$. The impact parameter $d$, as defined in Eq. (\ref{['defimpact']}), is negative.
• Figure 2: Variation of the elliptic flow $v_2$ with the Knudsen number, ${\rm Kn}$, for several values of the dilution parameter $D$. The statistical error on each point is $\delta v_2=7\times 10^{-4}$. For each value of $D$, Monte-Carlo results are fitted using Eq. (\ref{['simpleformula']}).
• Figure 3: Time dependence of the average elliptic flow $v_2$ from the transport model, from the corresponding 2-dimensional hydro calculation, and from usual 3-dimensional hydro with Bjorken longitudinal expansion.