SPheRIO is the name of a numerical implementation of hydrodynamic model of nucleus-nucleus collisions based on Smoothed Particle Hydrodynamics (SPH) method. The code has been investigated and developed within the São Paulo - Rio de Janeiro Collaboration. SPheRIO is the shorthand of Smoothed Particle hydrodynamical evolution of Relativistic heavy-IOn collisions.

Presentation and history


What is the Smoothed Particle Hydrodynamics (SPH)?

The SPH algorithm was first introduced for astrophysical applications, and later the method was extended to heavy ion collisions by the use of the variational approach. The main references for the SPH method in heavy ion collisions are

The method parameterizes the matter flow in terms of discrete Lagrangian coordinates, called SPH particles. In terms of SPH degrees of freedom, the equations of motion can be derived by using the variational principle. The main advantage of the method is that it is rather robust to deal with any kind of geometrical structure and violent dynamics. For example, shock wave phenomena can be treated without numerical difficulty, provided the size of SPH particles is appropriately chosen.

What is SPheRIO?

SPheRIO is the code which implements the entropy representation of the SPH model for relativistic high-energy collisions. It has investigated and developed within the São Paulo - Rio de Janeiro Collaboration. A general overview of SPheRIO can be found in

Initial conditions (IC)

Hydrodynamic models employ the hypothesis that hot and dense matter created in collisions reaches at a certain instant a local thermal equilibrium, after which it expands and cools down before particle emission takes place. Such a local thermal equilibrium is usually characterized by some IC, which can be expressed in terms of distributions of the fluid velocity and of thermodynamical quantities for a given time-like parameter.

In SPheRIO, one may employ different types of IC, such as Glauber type IC, which are based on a parameterization determined by single particle distributions, or on an event generator derived from some microscopic model.

What is the NeXus+SPheRIO?

It is a conjunction of NeXus and SPheRIO. NeXus provides the IC, and SPheRIO deals with hydrodynamic evolution part.

Equation of state (EOS)

In order to close the system of hydrodynamic equations, one also needs the EOS of the fluid, which describes the thermodynamic property of the fluid. In SPheRIO, several sets of pre-defined EOS are at disposal. The first set of EOS makes use of hadronic resonance model with finite volume corrections to describe the matter on the hadronic side, and MIT bag model for quark gluon plasma (QGP) phase. The main part of observed resonances in Particle Data Tables are included in the hadronic phase. Others include EOS with a fit to reproduce the lattice QCD data by Pasi Huovinen, EOS with a phenomenological critical point inspired by lattice QCD data and EOS taking into account local strangeness neutrality. Also some simple EOS are provided for testing purposes, for instance, a set of analytic EOS which assumes a massless pion gas in the hadronic phase and the MIT bag model in the QGP phase.

Freeze out

With the system expanding and cooling down, the constituent particles will eventually reach the stage where they do not interact with each other, until they reach the detectors. This is the decoupling stage of the hydrodynamic model. SPheRIO can be configured to adopt three different freeze-out scenarios, namely, thermal freeze-out, thermal and chemical freeze-out, and a continuous emission (CE).


A modified version of ThermInAtor is employed to handle hadronic decay.


  • Version 3.1
    • EOS with a phenomenological critical point inspired by lattice QCD data
    • EOS fit to lattice QCD data by Pasi Huovinen
    • Calculation of HBT radii
  • Version 3.0
    • Standalone build
    • EOS with local strangeness neutrality
    • Chemical freeze-out
    • Connection with TermInAtor
  • Version 2.0
    • EOS taking into account main part of observed resonances in Particle Data Tables
    • Continuous emission
  • Version 1.0
    • The main functionality
    • Equation of Motion (EOM) and List-Linked-Method
    • Thermal freeze-out

Main contributors

Instruction and examples on Installation

See Installation instruction for more information.


  • Version 3.1 (FORTRAN) Version 3.1 of SPheRIO (update files only)
  • Version 3.0 (FORTRAN) Standalone version of SPheRIO (with EOS 1st order phase transition with strangeness)
  • Version 3.0 (FORTRAN) Standalone version of SPheRIO (without EOS tables)

Manual of SPheRIO

The present manual of SPheRIO version 3.0 can be found here.

Useful Links


Yogiro Hama, Takeshi Kodama, Sandra Padula, Frédérique Grassi,Otávio Socolowski Jr.,Wei-Liang Qian

-- WlQian - 03 August 2013

Topic revision: r18 - 2013-08-03 - WlQian

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