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

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. (C) 1996 Acoustical Society of America.