ASA San Diego 1 Reverberated sound field modelling in coupled rooms using a diffusion equation Alexis Billon a, Vincent Valeau a, Anas Sakout a, Judical Picaut b a LEPTAB, University of La Rochelle, France b LCPC, Nantes, France 148 th Meeting of Acoustical Society of America San Diego, 17th november 2004 ASA San Diego 2 Model Presentation (1) The diffuse field assumption in closed spaces assumes that sound energy is uniform in the field. This is wrong especially for complex closed spaces or long rooms Diffusion equation for acoustic energy density w ( room mean free path, c sound speed) Diffusion coefficient with Recent works [Picaut et al, Acustica 83,1997] proposed an extension of the concept of diffuse sound field: This concept allows non-uniform energy density Diffusion Model Modelling Statistical theory Positions of the source and the coupling aperture Global sound absorption Source room absorption Synthesis Conclusion ASA San Diego 3 Model Presentation (2) Scope of this work: application for coupled rooms, for evaluating: stationary responses; impulse responses; comparison with statistical theory-based results. It has been applied successfully analytically for 1-D long rooms or streets [Picaut et al., JASA 1999] wall ( ) Sound absorption at walls is taken into account by an exchange coefficient [Picaut et al., Appl. Acoust. 99]: Diffusion Model Modelling Statistical theory Positions of the source and the coupling aperture Global sound absorption Source room absorption Synthesis Conclusion ASA San Diego 4 Modelling room acoustics with a diffusion equation (1) Room boundary (Fourier type condition) Source Source roomReceiving room DRhRDRhR DShSDShS Diffusion Model Modelling Statistical theory Positions of the source and the coupling aperture Global sound absorption Source room absorption Synthesis Conclusion ASA San Diego 5 Modelling room acoustics with a diffusion equation (2) Simulated geometry (dimensions in cm) Simulations characteristics: - Unstructured mesh with about 3000 nodes; - stationnary responseSound intensity Level Computing time: less than 1 minute; - impulse responseSound decay Computing time: less than 8 minutes. Diffusion Model Modelling Statistical theory Positions of the source and the coupling aperture Global sound absorption Source room absorption Synthesis Conclusion ASA San Diego 6 Statistical theory model of coupled rooms Source room ( S ) Receiving room ( R ) sound source Coupling aperture EsEs ERER mean energy densities Power balance for the two rooms coupling factor 0< k R