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

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.