vishnew

viscous 2+1D Israel-Stewart hydrodynamics for relativistic heavy-ion collisions

Attribution

I am not the author of this software: it was originally written by Dr. Huichao Song and further modified and enhanced by Zhi Qiu, Chun Shen, and Jia Liu. Alternate versions may be found at https://github.com/chunshen1987/VISHNew and https://github.com/JiaLiu11/iEBE/tree/hydro/EBE-Node/VISHNew.

Some references:

• http://inspirehep.net/record/771325
• http://inspirehep.net/record/785597

Usage

This is a stripped down and cleaned up version of the Ohio State University viscous 2+1D hydrodynamics code. I started from Jia Liu's version including shear and bulk viscosity at https://github.com/JiaLiu11/iEBE/tree/hydro/EBE-Node/VISHNew, however this repository does not share git history with Jia's because I used git filter-branch to remove a number of large files from old commits.

I made this version with one task in mind: running hydro as part of an event-by-event hybrid model, i.e. to be preceded by a Monte Carlo initial condition model and followed by particlization and hadronic transport models.

To compile and install, follow the standard CMake sequence:

mkdir build && cd build
cmake ..
make install

This will place several files in <prefix>/vishnew: the compiled binary vishnew, configuration file vishnew.conf, and equation of state table eos.dat.

Equation of state

The EOS table is generated at build time by the script eos/generate-eos-table.py, which connects a hadron resonance gas EOS at low temperature to a lattice EOS (HotQCD, http://inspirehep.net/record/1307761) at high temperature. Run ./generate-eos-table.py --plot to visualize several important thermodynamic quantities.

The EOS table has columns

energy_density  pressure  entropy_density  temperature

in natural units of GeV and fm. It has 100000 rows with evenly-spaced energy density steps, as expected by the vishnew code.

Configuration

The config file vishnew.conf has brief comments for each parameter. Note that the code expects the parameters in a specific order, so do not change the order of parameters in the config file. Parameters may also be passed on the command line with a key=value syntax, e.g.

vishnew Edec=0.30

Temperature-dependent viscosities

The shear viscosity is parametrized as

(eta/s)(T) = min + slope*(T - Tc) * (T/Tc)^curvature

for T > Tc = 0.154 GeV, where min, slope, and curvature are input parameters. The min and slope must be non-negative; curvature may be negative but probably not below -1, since this would cause decreasing (eta/s)(T).

For T < Tc (HRG phase), eta/s is constant, controlled by a single input parameter.

These parameters may be set in the config file or on the command line with keys etas_hrg, etas_min, etas_slope, etas_curv.

The bulk viscosity is parametrized as a Cauchy distribution with its peak at Tc and tunable max and width:

(zeta/s)(T) = max / (1 + ((T - Tc)/width)^2)

The max and width may be set in the config file or on the command line with keys zetas_max, zetas_width.

Running initial conditions

By default (with option InitialURead = 1), the initial energy density, flow, and shear viscous tensor must be provided. Place the following files in the vishnew folder:

• ed.dat - energy density
• u{1,2}.dat - flow velocity in x and y directions
• pi{11,12,22}.dat - components of the shear tensor (the remaining components are computed internally)
• The bulk pressure is computed internally as the deviation from ideal pressure, Π = e/3 - p(e).

If InitialURead = 0, only the energy density is required. Alternatively, set IEin = 1 and provide the entropy density sd.dat.

All files must contain square block-style grids and nothing else (comments will not work). The grid size depends on the LS (lattice size) parameter: grid size = 2*LS + 1. The grid step is hard-coded to 0.1 fm. So e.g. with the default LS = 130, the grid is 261x261 from -13 to +13 fm.

During time evolution, the code prints out a line for each timestep

 timestep_number  tau  max_energy_density  max_temperature

Evolution stops after the max energy density drops below the configured decoupling energy density.

The only output file is the hypersurface data surface.dat, beginning with a commented header containing the thermodynamic freeze-out quantities

# e = <energy density>
# p = <pressure>
# s = <entropy density>
# T = <temperature>

and followed by data columns

tau x y dsigma^t dsigma^x dsigma^y v_x v_y pi00 pi01 pi02 pi11 pi12 pi22 pi33 PI

where each row represents a volume element. All units are GeV and fm.

Note: The normal vector dsigma is output in contravariant form (index raised). Previous versions output the covariant vector (index lowered).