Numerical model for moderately nonlinear sound propagation in three-dimensional structures

Abstract

A three-dimensional numerical model is presented that is capable of handling moderately nonlinear sound propagation. The model is based on a finite-difference time-domain (FDTD) discretization of a set of equations that approximate the Navier–Stokes equations and that include molecular relaxation processes. The mathematical model and numerical discretization focus on compatibility with earlier linear FDTD models. In this way combining both models in a single simulation is trivial and optimum efficiency is obtained for acoustic propagation. A staggered grid is used for the discretization. Nonlinear effects, heat conduction, and damping are treated to a lower order of accuracy. Two examples illustrate the use of the model. The first example is the nonlinear resonance of a finite length duct. Typical waveform steepening and frequency shift, broadening, and skewing of the resonance peak that are also observed in experiments are found. The second example is a tuned reactive muffler installed on a duct. The decrease in insertion loss for high sound pressures is observed. Possibilities for future study are outlined.