# Elliptic flow

Huichao Song, 05/17/08

Differential elliptic flow v2(pt) for gluons for ideal and viscous hydro (HS+UH, VISH2+1 with full I-S eqns.):
(dotted line shows flow effects only and neglects viscous correction of distribution fct.)

The curves are also labelled by the grid sizes in numerical calculation. For example, ${\displaystyle 0.1-0.04}$ means ${\displaystyle \Delta x=\Delta y=0.1}$ fm, ${\displaystyle \Delta \tau =0.04}$ fm/c.

This figure was updated by H.S. on 09/08/2008 by using totally identical initialization for H&S and R&R eqns, old figure and explanaton could be found at Note for elliptic flow

The figure above was updated on 08/04/2008 by H.S. to include an comparison between different full I-S eqn:

• full I-S eqn-(R&R): ${\displaystyle \Delta _{j}^{m}\Delta _{k}^{n}{\dot {\pi }}^{jk}=-{\frac {1}{\tau _{\pi }}}(\pi ^{mn}{-}2\eta \sigma ^{mn})+{\frac {1}{2}}\pi ^{mn}\left(5D(\ln T)-\partial _{k}u^{k}\right)}$
• full I-S eqn-(S&H):${\displaystyle \Delta _{j}^{m}\Delta _{k}^{n}{\dot {\pi }}^{jk}=-{\frac {1}{\tau _{\pi }}}(\pi ^{mn}{-}2\eta \sigma ^{mn})-{\frac {1}{2}}\pi ^{mn}{\frac {\eta T}{\tau _{\pi }}}d_{k}\left({\frac {\tau _{\pi }}{\eta T}}u^{k}\right)}$

The figure above was updated on 7/23/2008 by H.S. to include an ideal hydro curve (light blue) from AZHYDRO which differs from VISH2+1 by an additional time splitting step in the transport algorithm (which should make it more accurate).

Other formats and data tables for this figure can be downloaded here: Au-global-0508.tar

Differential elliptic flow

Kevin Dusling, 7/1/2008

Comparison of v2 for models of KD+DT and HS+UH The above curves show the comparison of v2(pt) for the models of Song/Heinz and Dusling/Teaney. The uppermost curves are for ideal hydrodynamics. The middle curves show the v2 spectra with the viscous correction to the distribution function (fo only). The last set of curves (labeled fo + \delta f) show the full viscous result for \eta/s=0.08.

The raw data for Dusling/Teaney is here:
Ideal
Viscous