Finite Element Modeling of Woodwind Instruments

The input impedance of simple woodwind-like instruments is evaluated using the Finite Element Method (FEM) and compared to theoretical calculations based on the transmission-matrix method (TMM). Thermoviscous losses are accounted for with an impedance boundary condition based on acoustic boundary layer theory. The systems are surrounded by a spherical radiation domain with a second-order non-reflecting spherical-wave boundary condition on its outer surface. For simple geometries, the FEM results are shown to match theory with great accuracy. When considering toneholes, boundary layer losses must be added to the TMM model to achieve good agreement with the FEM calculations. For geometries with multiple closed or open toneholes, discrepancies between the FEM and the TMM results become more significant and appear related to internal or external interactions. For closed side holes, this effect is more important at low frequencies, thus affecting the first few resonances. For open side holes, this effect is particularly important near the tonehole cutoff frequency but extends to lower frequencies as well. In general, the TMM does not model tonehole interactions, thus posing a limitation to its accuracy