Numerical simulation of timpani
Patrick Joly, Leïla Rhaouti, Antoine J. Chaigne · The Journal of the Acoustical Society of America · 1999
The goal of this work is to achieve sound synthesis via time-domain numerical simulations, with particular interest in the case of timpani. The approach combines the use of a mathematical model, which is supposed to represent accurately the physics of the phenomena, and of modern techniques for the approximation of partial differential equations. The model appears as a system of wavelike equations coupled by fluid–solid interaction conditions. It includes various damping mechanisms as well as a nonlinear model for the mallet–membrane interaction. The numerical approach aims at realizing the best compromise among accuracy, stability, and efficiency. Its main characteristics are the use of finite elements for the space discretization, of a fictitious domain method for a flexible treatment of the geometry of the instrument, and of explicit centered finite differences for the time discretization. Higher-order absorbing boundary conditions are used for simulating the radiation of sound in free space. In the presentation, the main properties of the numerical methods will be emphasized and various numerical results will be compared to experiments.