TIME DOMAIN SIMULATION FOR SOUND PROPAGATION OVER VARIOUS OBJECTS AND UNDER VORTICAL BACKGROUND CONDITIONS

Abstract

Acoustic wave propagations have been studied for a long time with both experimental and numerical methods. Most of the analytical solutions for wave propagations are considered for simple environments such as a homogeneous atmospheres. As a result, the analytical solutions are unable to be applied for complicated environments. Numerical methods have become more and more important in acoustics studies after decades of development. The finite difference time-domain method (FDTD) is one of the most commonly used numerical methods in wave propagation studies. Compared with the other methods, the FDTD method is able to include many aspects of sound wave behaviors such as reflection, refraction, and diffraction in the physical problems. In this thesis, the linearized acoustic Euler equations coupled with the immersed boundary method are applied to investigate the sound wave propagation over complex environments. For the three-dimensional simulations of sound wave propagation in long distance, the moving domain method and parallel computing techniques are applied. Based on these approaches, the computational costs are significantly reduced and the simulation efficiency is greatly improved. When looking into the effects of high subsonic vortical flow, a high order WENO scheme is applied for the simulation. In this way the simulation stability can be achieved and the sound scattering of vortical flow can be studied. Then, the numerical scheme is applied to simulate an ultrasonic plane wave propagating through biological tissue. The linearized Euler acoustic equations coupled with the spatial fractional Laplacian operators are used for numerical simulations. The absorption and attenuation effects of the biological lossy media are successfully observed from the simulation results. Throughout this thesis, the simulation results are compared with either experimental measurements or analytical solutions so that the accuracy of the implemented numerical scheme is validated.