Vienna Talk 2015 on Music Acoustics
“Bridging the Gaps”     16–19 September 2015


Discrete-time conserved quantities for damped oscillators

Chatziioannou, Vasileios and Van Walstijn, Maarten 

Proceedings of the Third Vienna Talk on Music Acoustics (2015), pp. 135–139


Numerical sound synthesis is often carried out using the finite difference time domain method. In order to analyse the stability of the derived models, energy methods can be used for both linear and nonlinear settings. For Hamiltonian systems the existence of a conserved numerical energy-like quantity can be used to guarantee the stability of the simulations. In this paper it is shown how to derive similar discrete conservation laws in cases where energy is dissipated due to friction or in the presence of an energy source due to an external force. A damped harmonic oscillator (for which an analytic solution is available) is used to present the proposed methodology. After showing how to arrive at a conserved quantity, the simulation of a nonlinear single reed shows an example of an application in the context of musical acoustics.


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  • energy conservation
  • physical modelling
  • finite differences

  • Status
    Invited Paper
    reviewed paper

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