Conservative 1D propagation in horns with mobile walls: power-balanced space–time discretization and simulation of the vocal tract

Authors

Colette Voisembert, Thomas Hélie, Victor Wetzel, Fabrice Silva

Abstract

              This paper models and simulates conservative linear acoustic propagation in axisymmetric pipes with time–space-dependent cross-sections. It extends the horn equation to moving-wall bores. The physical equations (partial differential equations) satisfy a power balance, allowing their formulation as a Port-Hamiltonian system. A two-step numerical method is proposed, which preserves mass, momentum and power conservation in discrete domains. Spatial discretization yields a system of Ordinary Differential Equations (ODE) that satisfies known acoustic characteristics for static walls and ensures power-balanced propagation for controlled dynamic walls. Time discretization via the discrete-gradient method results in a discrete time–space model. Simulations validate conservative propagation and resonances for static walls and capture dynamic vocal tract acoustics during articulation.

Citation

• Journal: IMA Journal of Mathematical Control and Information
• Year: 2025
• Volume: 42
• Issue: 4
• Pages:
• Publisher: Oxford University Press (OUP)
• DOI: 10.1093/imamci/dnaf039

BibTeX

@article{Voisembert_2025,
  title={{Conservative 1D propagation in horns with mobile walls: power-balanced space–time discretization and simulation of the vocal tract}},
  volume={42},
  ISSN={1471-6887},
  DOI={10.1093/imamci/dnaf039},
  number={4},
  journal={IMA Journal of Mathematical Control and Information},
  publisher={Oxford University Press (OUP)},
  author={Voisembert, Colette and Hélie, Thomas and Wetzel, Victor and Silva, Fabrice},
  year={2025}
}

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