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0001 *******************************************************************************
0002 *                                                                             *
0003 *            vHLLE : a 3D viscous hydrodynamic code                           *
0004 *            by Iurii Karpenko                                                *
0005 *  For the detailed description please refer to:                              *
0006 *  Comput. Phys. Commun. 185 (2014), 3016    [arXiv:1312.4160]                *
0007 *                                                                             *
0008 *  This code can be freely used and redistributed, provided that this         *
0009 *  copyright appear in all the copies. If you decide to make modifications    *
0010 *  to the code, please contact the authors, especially if you plan to publish *
0011 *  the results obtained with such modified code. Any publication of results   *
0012 *  obtained using this code must include the reference to:                    *
0013 *  Comput. Phys. Commun. 185 (2014), 3016    [arXiv:1312.4160]                *
0014 *                                                                             *
0015 *******************************************************************************
0016 
0017 
0018  This package contains source code of vHLLE.
0019  To get familiar with the code please use 'cpc_final' branch.
0020  
0021  The description below applies for the 'cpc_final' branch of the code.
0022  
0023  
0024  0. BRIEF DESCRIPTION OF THE PACKAGE
0025  
0026  The package contains the following files:
0027  Makefile
0028  src/      : source subdirectory
0029   |- inc.h : predefined constants
0030   |- rmn.h, rmn.cpp : transformation procedures from conserved variables to
0031   |                   primitive variables and back
0032   |- cll.h, cll.cpp : Cell class which stores and manipulates the properties of
0033   |                   the individual hydro cell
0034   |- eos.h, eos.cpp : EoS class, equation of state information
0035   |- fld.h, fld.cpp : Fluid class, which contains fluid (3D array of fluid cells)
0036   |                   as a whole and performs auxiliary actions on a fluid
0037   |- ic.h, ic.cpp : initial conditions for fluid-dynamical evolution from
0038   |                 optical Glauber or Guber flow
0039   |- s95p.h, s95p.cpp: manages tabular initial conditions and EoS 's95' (for optional use)
0040   |- trancoeff.h, trancoeff.cpp : Trancoeff class containing transport
0041   |                               coefficients: (T-dependent) shear, bulk
0042   |                               viscosites and corresponding relaxation times
0043   |- hdo.h, hdo.cpp : Hydro class, which contains the algorithms of hydrodynamic solution
0044   \- main.cpp : main() function, initializes all the objects and calls ecolution
0045                 loop, also takes care of reading the parameters of the
0046                 simulation from parameter file
0047  params/  : subdirectory with parameter files, see their description below
0048  eos/Laine_nf3.dat : equation of state, latticeQCD inspired results
0049                      from M. Laine and Y. Schroder, PRD 73, 085009
0050  ic/      : sample tabulated initial conditions, used for 3D run
0051  hydro_output/  : subdirectory containing hydrodynamic optput (generated by the
0052                   code) and Gnuplot scripts to make some of the plots presented
0053                   in the paper. See the description in Sect. II below.
0054 
0055 
0056  I. BUILDING vHLLE on Linux
0057 
0058  1) The following software must be installed in order to compile the code:
0059  make, g++, binutils, ROOT
0060  
0061  To install those packages,
0062  -> on Ubuntu 11.x - 14.x run:
0063  sudo apt-get install make g++ binutils root-system
0064  -> on Fedora 18 and above run: 
0065  sudo yum install make gcc binutils root
0066  
0067  The latest version of the ROOT package is also available at http://root.cern.ch/
0068  
0069  Optionally, to run Gluplot scripts provided in the program package one has to
0070  install Gnuplot and awk (gawk).
0071   
0072  2) Unpack the code: 
0073  mkdir vHLLE
0074  tar xzf vHLLE.tar.gz -C vHLLE
0075  cd vHLLE
0076 
0077  3) make the code:
0078  make
0079  
0080  
0081  II. RUNNING vHLLE
0082  
0083  1. to run the code, type
0084  ./hlle_visc <parameter-file>
0085  
0086  Sample parameter files are located in "params" subdirectory. They cover several
0087  of the presented results:
0088 
0089  1) comparison to VISH2+1 code in Section 4.3 ("Matter expansion in heavy ion
0090   collisions"). The corresponding parameter files are:
0091 params/song2DCPC.*
0092 The filename suffixes correspond to:
0093  b0 = impact parameter 0 fm
0094  b7 = impact parameter 7 fm
0095  etas008 = viscous hydro simulation with eta/s=0.08
0096  ideal = ideal hydro simulation
0097  
0098  In order to reproduce the comparison plots (Figures 9, 10) one should run the
0099  code with all 4 input files. This will create subdirectories "song2D.*" with 
0100  hydrodynamic output for each parameter set. Then Gunplot scripts hydro_output/*.plot 
0101  will read and parse the hydrodynamic output and draw the corresponding plots.  
0102  Then run Gnuplot with "hydro_output" as working directory, and load one of the 
0103  scripts in Gnuplot prompt:
0104 
0105  cd hydro_output
0106  gnuplot
0107  gnuplot> load 'radFlow.plot'  # which creates "vradSong.eps" postscript containing Figure 9,
0108  gnuplot> load 'epsilonp.plot'  # which creates "epsilonpSong.eps" postscript containing Figure 10
0109  
0110  2)numerical solution for ideal Gubser flow (end of Section 4.1).
0111   The corresponding parameter file is:
0112 params/gubserCPC
0113 
0114  To produce the plots run Gnuplot with "hydro_output" as working directory. In Gnuplot prompt, type:
0115  gnuplot> load 'gubser.plot'
0116  which creates "gubserEps.eps" and "gubserVx.eps", which are Figures 5 and 6,
0117  respectively.
0118 
0119  3)3D hydro simulation described in Section 4.4 ("Energy conservation").
0120   The corresponding parameter file is:
0121 params/3DCPC
0122 
0123  Note that this simulation uses full 3D grid. With the parameters provided, the 
0124  program consumes about 1900 Mbytes of RAM. Therefore please make sure that the 
0125  host machine has enough RAM to run this simulation.
0126 
0127  The purpose of this simulation is to check the energy/entropy conservation 
0128  during 3D hydrodynamic expansion of a closed system. The corresponding results 
0129  are presented in Table 1 of the paper. To reproduce the results, please watch 
0130  the console output of the program, which contains total energy and total entropy 
0131  after each timestep.
0132  Note that by default the code uses the equation of state 'p=epsilon/3'. 
0133  To reproduce the numbers in the middle column of the Table 1 corresponding to 
0134  'Laine' EoS, please recompile the code with  'EXTRA_FLAGS   = -D TABLE' in Makefile.
0135  The typical console output of the program is the following:
0136  
0137 -----
0138 .....
0139 step= 0  dtau= 0.05
0140 
0141 calcTotals: E =        1402.31  Efull =        1402.33
0142            Px =              0      S =        6869.23
0143 .....
0144 ------
0145 where
0146       E : total energy of the system [GeV], computed from ideal part of the
0147           energy-momentum system only,
0148   Efull : total energy of system including viscous terms in energy-momentum tensor,
0149      Px : x-component of the total momentum
0150       S : total enrgopy including viscous terms
0151 
0152 
0153  III. STRUCTURE OF THE OUTPUT FILES
0154  
0155  Each hydrodynamic simulation records its results in a separate directory, which 
0156  is specified by the value of 'outputDir' parameter in the corresponding parameter 
0157  file. Below we denote the cells used for the output as  cell(ix,iy,iz), where
0158  ix=[0...nx-1]  is x-coordinate of cell on 3D grid
0159  iy=[0...ny-1]  is y-coordinate of cell on 3D grid
0160  iz=[0...nz-1]  is z-coordinate of cell on 3D grid
0161 
0162  As a result of the simulation the output directory contains the following files:
0163  outx.dat    :   distributions in cells along X direction at every timestep.
0164                  The cells used are cell(ix,ny/2,nz/2),  ix=0...nx-1
0165  outy.dat    :   distributions in cells along Y direction at every timestep.
0166                  The cells used are cell(nx/2,iy,nz/2),  iy=0...ny-1
0167  outz.dat    :   distributions in cells along Z direction at every timestep.
0168                  The cells used are cell(nx/2,ny/2,iz),  iz=0...nz-1
0169  outdiag.dat :   distributions in cells along diagonal direction in XY plane
0170                  at every timestep. The cells used are cell(ix,ix,iz), ix=0...nx-1
0171                  Works reliabaly if nx=ny
0172  out.aniz.dat:   grid-integrated quantities $\epsilon_p$, $\epsilon_p'$ 
0173                  (see Subsection 4.3 "Matter expansion in ...")
0174  
0175  The format of the columns in the output files is:
0176  
0177  outx.dat:
0178  t  x  vx  vy  eps  nb  T  mub  [pi*10]  Pi  cut_flag
0179  
0180  outy.dat:
0181  t  y  vy  vx  eps  nb  T  mub  [pi*10]  Pi  cut_flag
0182 
0183  outz.dat:
0184  t  z  vz  vx  eps  nb  T  mub  [pi*10]  Pi  cut_flag
0185 
0186  outdiag.dat:
0187  t  sqrt(x*x+y*y)  vx  vy  eps  nb  T  mub  [pi*10]  Pi  cut_flag
0188  
0189  out.aniz.dat:
0190  t  <vt>  <epsilon_p>  <epsilon_p'>
0191  
0192  where
0193  t : proper time [fm/c]
0194  x : x coordinate [fm]
0195  y : y coordinate [fm]
0196  z : rapidity
0197  vx : x-component of 3-velocity
0198  vy : x-component of 3-velocity
0199  vz : longitudinal flow rapifity
0200  eps : energy density in fluid rest frame [GeV/fm^3]
0201  nb : baryon density in fluid rest frame [1/fm^3]
0202  T  : temperature [GeV]
0203  mub : baryon chemical potential [GeV]
0204  [pi*10] : $\pi^{mu\nu}$ components: $\pi^{\tau\tau}$, $\pi^{\tau x}$, 
0205            $\pi^{\tau y}$, $\pi^{\tau\eta}$, $\pi^{xx}$, $\pi^{xy}$, $\pi^{x\eta}$, 
0206            $\pi^{yy}$, $\pi^{y\eta}$, $\pi^{\eta\eta}$. All the components 
0207            correspond to $\tilde{\pi^{\mu\nu}}$, see Section 2. Unirs are [GeV/fm^3]
0208  Pi : bulk pressure [GeV/fm^3]
0209  cut_flag : viscous corrections are cut by cut_flag factor in the cell 
0210             (not cut if cut_flag = 1.0)