SPPS is a sound particles-tracing code, based on geometrical, energetical and probabilistic approaches.


The simulation principle of the SPPS code (from French "Simulation de la Propagation de Particules Sonores") relies upon tracking sound particles, carrying a amount of energy ε and emitted from a sound source, within a 3D-domain. Each particle propagates along a straight line between two time steps Δt (the whole trajectory may be curved), until collision with an object. At each collision, sound particles may be absorbed, reflected, scattered, diffused, transmitted, depending on the nature of the object.

Two algorithms can be considered:

  • The first approach (Energetic) is to consider that the energy of the particle is constant. In function of the phenomena, the particle may disappear from the domain or follows its propagation: the number of sound particles decreases along the time.
  • In the second approach (Random), the particle energy is varying according to the physical phenomena occurring during the propagation. In this case, the number of particles in the domain should be constant along the time.

Since, in both cases, physical phenomena can be modeled according to probabilistic laws, both approaches are equivalent to Monte-Carlo methods. The accuracy of prediction is then mainly dependent of the initial number of particles.


The SPPS code was developed and is still maintained by the Environmental Acoustics Research Unit of Université Gustave Eiffel (formerly Ifsttar, formerly LCPC) since 2001. The initial version was developed with MATLAB, thus in C++ since 2007.

Application domains
  • ROOM ACOUSTICS: sound propagation in a room, calculation of room acoustic parameters
  • BUILDING ACOUSTICS: coupled rooms, sound propagation in a building
  • URBAN ACOUSTICS: sound propagation in a street
Advantages of the current version
  • Very detailed representation of the direct field, reflected field, diffuse field
  • Include most of physical phenomena (wall absorption and transmission, atmospheric absorption, diffusion by fitting objects, celerity profile)
Limitations of the current version
  • Diffraction (reflector, edge...) is not taken into account
  • Computational time can increase greatly depending of the number of sound particles, the calculation method (energetic), the number of sound sources, the considered physical phenomena (transmission), the king of geometry (many rooms, outdoor propagation, very large spaces)
  • No exact description of the direct field and specular reflections

A full documentation of the SPPS method in available online: https://i-simpa-wiki.readthedocs.io/fr/latest/code_SPPS.html

Team references
  • Picaut, Judicaël, and Nicolas Fortin. “SPPS, a Particle-Tracing Numerical Code for Indoor and Outdoor Sound Propagation Prediction.” In Acoustics 2012 Nantes, 1417–22. Nantes, France: Société Française d’Acoustique, 2012. http://hal.archives-ouvertes.fr/hal-00810894.
  • Picaut, Judicaël. “Application Numérique Du Concept de Particules Sonores à La Modélisation Des Champs Sonores En Acoustique Architecturale.” BULLETIN DES LABORATOIRES DES PONTS ET CHAUSSÉES, no. 258–259 (October 2005). English version available.