Numerical simulation of sound propagation in and around ducts using thin boundary elements

Abstract

Investigating the sound field in and around ducts is an important topic in acoustics, e.g. when simulating musical instruments or the human vocal tract. In this paper a method that is based on the boundary element method in 3D combined with a formulation for infinitely thin elements is presented. The boundary integral equations for these elements are presented, and numerical experiments are used to illustrate the behavior of the thin elements. Using the example of a closed benchmark duct, boundary element solutions for thin elements and surface elements are compared with the analytic solution, and the accuracy of the boundary element method as function of element size is investigated. As already shown for surface elements in the literature, an accumulation of the error along the duct can also be found for thin elements, but in contrast to surface elements this effect is not as big and a damping of the amplitude cannot be seen. In a second experiment, the impedance at the open end of a half open duct is compared with formulas for the radiation impedance of an unflanged tube, and a good agreement is shown. Finally, resonance frequencies of a tube open at both ends are calculated and compared with measured spectra. For sufficiently small element sizes frequencies for lower harmonics agree very well, for higher frequencies a difference of a few Hertz can be observed, which may be explained by the fact that the method does not consider dampening effects near the duct walls. The numerical experiments also suggest, that for duct simulations the usual six to eight elements per wavelength rule is not enough for accurate results.