An Energy Conserving Finite Difference Scheme for Simulation of Collisions

Vasileios Chatziioannou, Maarten Van Walstijn

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Nonlinear phenomena play an essential role in the sound production process of many musical instruments. A common source of these effects is object collision, the numerical simulation of which is known to give rise to stability
issues. This paper presents a method to construct numerical schemes that conserve the total energy in simulations of one-mass systems involving collisions, with no conditions imposed on any of the physical or numerical parameters.
This facilitates the adaptation of numerical models to experimental data, and allows a more free parameter adjustment in sound synthesis explorations. The energy preservedness of the proposed method is tested and demonstrated though several examples, including a bouncing ball and a non-linear oscillator, and implications regarding the wider applicability are discussed.
Original languageEnglish
Publication statusPublished - Jul 2013
EventSMC Sound and Music Computing Conference - Stockholm, Sweden
Duration: 30 Jul 201303 Aug 2013


ConferenceSMC Sound and Music Computing Conference

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