MD is a numerical code for the evaluation of reverberated fields in rooms, using the room acoustics Diffusion Model, and based on a statistical and energetical approach.
MD code is currently in an experimental version (MD_Octave). It is not included in the installation file, but is available in the I-Simpa GitHub repository (ExperimentalCore and ExperimentalScript). The Comsol version of the diffusion model (MD_Comsol), connected to I-Simpa, is not available.
The MD code (from French "Modèle de Diffusion") is an implementation of the room acoustics diffusion model. This model allows to evaluate the reverberated field using a transport process. Under some conditions, the model can be reduced to a diffusion process defined by a gradient equation (“Fick’s law”) and a diffusion equation for the sound energy density, with a main parameter called the diffusion coefficient. The diffusion model can also be seen as an extension of Sabine’s theory, and is mainly valid for purely diffuse reflections. From the initial approach proposed by Ollendorff (1969) and developed later by Picaut et al (1997), many developments have been carried out on the extension of the diffusion model: boundary conditions for wall reflections, atmospheric attenuation, coupling between rooms, diffusion in fitted rooms..
Ollendorff, F. “Statistical Room Acoustics as a Problem of Diffusion (a Proposal).” Acustica 21 (1969): 236–45.
- Elements of validation
- Quasi-cubic room with diffuse reflection and atmospheric absorption
- Cubic room with diffuse reflection and uniform absorption
- Cubic room with diffuse reflection and uniform absorption (0.1 and 0.5)
- Long room with diffuse reflection and uniform absorption
- Low room with diffuse reflection and non-uniform absorption
- Two coupled cubic rooms with or without a door in a separation wall
The MD code is maintained by the Environmental Acoustics Research Unit of Université Gustave Eiffel (formerly Ifsttar, formerly LCPC), since 2003 and is developed in collaboration with the Pprime Institute, the University of La Rochelle, and the Cerema, with the financial support of the French environment and energy management agency (ADEME). Since 2003, several experimental codes was developed, used the Femlab toolbox for Matlab and thus COMSOL* with I-Simpa in 2010. In order to be independent of proprietary software and to distribute the numerical code as widely as possible, the MD code that is embedded within I-Simpa is now using GNU Octave since 2018.
* Since 2005, COMSOL propose its own implementation of the room acoustics diffusion model. See for example this article: https://www.comsol.com/blogs/sweet-dreams-with-diffusion-acoustics/
- ROOM ACOUSTICS: reverberated sound field in a room, calculation of room acoustic parameters, coupled rooms
- URBAN ACOUSTICS: although some references show that the diffusion model can be used in urban areas, this is not implemented in the current release of the DM code.
Advantages of the current version
- Very fast overview of the sound field distribution in a multi-rooms environment
- Include most of physical phenomena (wall absorption and transmission, atmospheric absorption, diffusion by fitting objects)
Limitations of the current version
- Diffraction is not taken into account
- Wall are supposed perfectly diffuse
- No individual representation of first reflections (all contributions are included in the reverberated field)
- Valid for high reverberant sound field
The following references are only from the development team (see History section), for the room acoustics diffusion model:
- Foy, Cédric, Judicaël Picaut, and Vincent Valeau. “Including Scattering within the Room Acoustics Diffusion Model: An Analytical Approach.” In The Journal of the Acoustical Society of America, 140:2659–69. Boston, USA, 2017. https://doi.org/10.1121/1.4963081.
- Visentin, Chiara, Nicola Prodi, Vincent Valeau, and Judicaël Picaut. “Experimental Analysis of the Relationship between Reverberant Acoustic Intensity and Energy Density inside Long Rooms.” The Journal of the Acoustical Society of America 138, no. 1 (July 1, 2015): 181–92. https://doi.org/10.1121/1.4922334.
- Visentin, Chiara, Nicola Prodi, Vincent Valeau, and Judicaël Picaut. “A Numerical Investigation of the Fick’s Law of Diffusion in Room Acoustics.” The Journal of the Acoustical Society of America 132, no. 5 (2012): 3180-3189. https://doi.org/10.1121/1.4756924.
- Billon, Alexis, Judicaël Picaut, Vincent Valeau, and Anas Sakout. “Acoustic Predictions in Industrial Spaces Using a Diffusion Model.” Advances in Acoustics and Vibration 2012 (2012): 1–9. https://doi.org/10.1155/2012/260394.
- Foy, Cédric, Vincent Valeau, Alexis Billon, Judicaël Picaut, and Anas Sakout. “An Empirical Diffusion Model for Acoustic Prediction in Rooms with Mixed Diffuse and Specular Reflections.” Acta Acustica United with Acustica 95, no. 1 (2009): 97–105. https://doi.org/10.3813/AAA.918131.
- Billon, Alexis, Judicael Picaut, Cedric Foy, Vincent Valeau, and Anas Sakout. “Introducing Atmospheric Attenuation within a Diffusion Model for Room-Acoustic Predictions.” The Journal of the Acoustical Society of America 123, no. 6 (2008): 4040–43. https://doi.org/10.1121/1.2903872.
- Billon, Alexis, Cedric Foy, Judicael Picaut, Vincent Valeau, and Anas Sakout. “Modeling the Sound Transmission between Rooms Coupled through Partition Walls by Using a Diffusion Model.” The Journal of the Acoustical Society of America 123, no. 6 (2008): 4261–71. https://doi.org/10.1121/1.2905242.
- Billon, A., J. Picaut, and A. Sakout. “Prediction of the Reverberation Time in High Absorbent Room Using a Modified-Diffusion Model.” Applied Acoustics 69, no. 1 (January 2008): 68–74. https://doi.org/10.1016/j.apacoust.2007.03.001.
- Valeau, Vincent, Murray Hodgson, and Judicaël Picaut. “A Diffusion-Based Analogy for the Prediction of Sound Fields in Fitted Rooms.” Acta Acustica United with Acustica 93, no. 1 (2007): 94–105.
- Valeau, V., J. Picaut, and M. Hodgson. “On the Use of a Diffusion Equation for Room-Acoustic Prediction.” The Journal of the Acoustical Society of America 119, no. 3 (2006): 1504–13. https://doi.org/10.1121/1.2161433.
- Billon, Alexis, Vincent Valeau, Anas Sakout, and Judicael Picaut. “On the Use of a Diffusion Model for Acoustically Coupled Rooms.” The Journal of the Acoustical Society of America 120, no. 4 (2006): 2043–54. https://doi.org/10.1121/1.2338814.
- Picaut J., Simon L., and Polack J.-D. “Sound Field in Long Rooms with Diffusely Reflecting Boundaries.” Applied Acoustics 56, no. 4 (1999): 217–40. https://doi.org/10.1016/S0003-682X(98)00032-2.
- Picaut, J., L. Simon, and J.D. Polack. “A Mathematical Model of Diffuse Sound Field Based on a Diffusion Equation.” Acta Acustica United with Acustica 83, no. 4 (1997): 614–21.