Correction of computational artifacts in numerical solving of diffusion equation for room acoustics

Jaroslaw Kraszewski , Andrzej Dobrucki (1)

1 Wroclaw University of Science and Technology

In the paper a numerical algorithm for solving of diffusion equation in application for room acoustics is presented. The 1D, 2D and 3D models are considered. It has been observed that using simple FTCS algorithm for solving the diffusion equation, an additional energy is generated when the acoustic wave is reflected from the walls. The energy is doubled when the wave reflects from the surface, it is multiplied by 4 when the wave achieves an edge, and it is multiplied by 8 for reflection from the corner. This numerical phenomenon influences the calculated reverberation time. In 3D model the reverberation time is inconsistent with Sabine and Eyring formulae. The difference is about 50%. A heuristic modification of algorithm is proposed. Using this modified algorithm the additional energy is not generated and computed reverberation time differs from Sabine and Eyring formulas 6 – 10%.

Domaines: Acoustique [physics.class-ph]

Jaroslaw Kraszewski, Andrzej Dobrucki. Correction of computational artifacts in numerical solving of diffusion equation for room acoustics. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810754⟩