Time-domain simulation of a dissipative reed instrument
Résumé
Sound synthesis of reed wind instruments requires special care to ensure numerical stability and accuracy of the timedomain simulation. Energy-based methods have proven very efficient for this purpose, where the instrument model is split into several subsystems which exchange and dissipate a numerical analog of the physical energy. A wide range of reed, propagation, tone hole and radiation models may thus be coupled. Space discretization is performed using 1D spectral finite elements, offering an affordable, flexible and more accurate alternative to finite differences for computing propagation of the acoustic waves along the instrument's bore, and energy-consistent time-stepping schemes are used for numerical integration of the equations. Whenever implicit couplings are used to ensure energy consistency, algorithmic tricks allow us to update all the unknowns explicitly via algebraic elimination, such that in the end, no matrix inversion is required. We will present some of the models and numerical schemes implemented in our open-source software OpenWInD (openwind.gitlabpages.inria.fr/web), including a new model for approximating losses due to viscothermal boundary layers in the time domain. Simulation code will be made available in the toolbox OpenWInD under GPLv3.
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