Time-Domain Simulation of Sound Propagation in Frequency-Dependent Materials

Abstract

This dissertation investigates sound propagation in frequency-dependent materials. The study provides an improved understanding of how to numerically model the porous impedance materials more accurately under the conditions of complicated geometries. The finite difference time-domain (FDTD) method is implemented on the linearized Euler equation (LEE), along with the immersed boundary (IB) method and other numerical techniques to simulate the acoustic wave propagation in air, water, porous media and biological tissues. When material properties vary in the frequency domain, their time-domain counterpart may contain either convolution operation or fractional derivative operation. Both operations have been studied in this dissertation. Recursive algorithm methods, piece-wise constant recursive methods (PCRC) and piece-wise linear recursive methods (PLRC) are used to numerically solve for convolution operations, and fractional central difference (FCD) methods are used to solve for fractional Laplacians. Both methods show good results in comparison with analytical solutions. A variety of models have been implemented to simulate the acoustic wave propagation inside porous media. The techniques include: the Zwicker and Kosten (ZK) phenomenological model, the Delany and Bazley model, various porosity two-parameter models, the time-domain boundary condition (TDBC) models, and Wilson’s relaxation model (WRX). A new method is also proposed that utilizes the ANSI/ASA-S1.18 measurements to construct a new relaxation function. The new relaxation function can improve the prediction from the TDBC and WRX models significantly. The ZK and WRX models have also been used in predicting the noise reduction of a house. The noise due to transmission and vibration of the wall is modeled as a simple wave transmission through a porous material layer. A curve fitting method is used to match acoustic properties of the wall material. By assembling all the materials together, the over-all acoustic response of a house can be simulated. When acoustic wave propagating in biological tissues, wave propagation equations were previously solved either with convolutions, which consume a large amount of memory, or with pseudo-spectral methods, which cannot handle complicated geometries effectively. The approach described in this study employs FCD method, combined with the IB method for the FDTD simulation. It also works naturally with the IB method which enables a simple Cartesian-type grid mesh to be used to solve problems with complicated geometries. This work also studies acoustic scattering effects caused by 2D or 3D vortices. The LEE is used to investigate sound wave propagation over subsonic vortices. Instead of traditional direct numerical simulation (DNS) methods, the new approach treats vortex flow field as a scattering background flow and solves the acoustic field with the LEE solver. The numerical method uses a high-order WENO scheme to accommodate the highly convective background flow at high Mach numbers. The study focuses on the acoustic field scaling laws scattered by the 2D and 3D vortices.