A [formula omitted] dimensional viscous hydrodynamic code for relativistic heavy ion collisions

Abstract

We describe the details of 3+1 dimensional relativistic hydrodynamic code for the simulations of quark–gluon/hadron matter expansion in ultra-relativistic heavy ion collisions. The code solves the equations of relativistic viscous hydrodynamics in the Israel–Stewart framework. With the help of ideal–viscous splitting, we keep the ability to solve the equations of ideal hydrodynamics in the limit of zero viscosities using a Godunov-type algorithm. Milne coordinates are used to treat the predominant expansion in longitudinal (beam) direction effectively. The results are successfully tested against known analytical relativistic inviscid and viscous solutions, as well as against existing 2+1D relativistic viscous code. Program summaryProgram title: vHLLECatalogue identifier: AETZ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AETZ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 13825No. of bytes in distributed program, including test data, etc.: 92750Distribution format: tar.gzProgramming language: C++.Computer: any with a C++ compiler and the CERN ROOT libraries.Operating system: tested on GNU/Linux Ubuntu 12.04 x64 (gcc 4.6.3), GNU/Linux Ubuntu 13.10 (gcc 4.8.2), Red Hat Linux 6 (gcc 4.4.7).RAM: scales with the number of cells in hydrodynamic grid; 1900 Mbytes for 3D 160×160×100 grid.Classification: 1.5, 4.3, 12.External routines: CERN ROOT (http://root.cern.ch), Gnuplot (http://www.gnuplot.info/) for plotting the results.Nature of problem:relativistic hydrodynamical description of the 3-dimensional quark–gluon/hadron matter expansion in ultra-relativistic heavy ion collisions.Solution method:finite volume Godunov-type method.Running time:scales with the number of hydrodynamic cells; typical running times on Intel(R) Core(TM) i7-3770 CPU @ 3.40 GHz, single thread mode, 160×160×100 grid and p=ε/3 EoS (setup discussed in Sec. 4.4):7.6 sec/timestep for ideal hydro evolution;15.7 sec/timestep for viscous hydro evolution;37 sec/timestep for tabulated EoS and ideal hydro evolution.