Abstract
A very simplified model for the clarinet consists in a system of two coupled 1D PDE’s of fluid mechanics-acoustics, expressing the wave equation with the unknowns velocity and pressure with reflection at the boundaries. No damping is taken into account and the reed model is highly simplified. Two numerical schemes are considered. The first one based on staggered grids does not dissipate with the maximal time step satisfying the CFL condition. The second one, using only one grid, is dissipating due to upstream weighting. An energy estimate is proved because of the numerical formulation which is suited to the boundary conditions.
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References
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Prignet, A. (2017). Simplified Model for the Clarinet and Numerical Schemes. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects . FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-57397-7_40
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DOI: https://doi.org/10.1007/978-3-319-57397-7_40
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