Source and boundary conditions in finite difference time domain modelling of room acoustics

Jeong, H

Abstract

This project deals with several issues on the use of Finite Difference Time
Domain (FDTD) method for room acoustic simulation. The main features covered
are: source implementation; modeling of frequency dependent boundary conditions;
and modeling of arbitrary wall geometry and associated errors in stair-case
approximations.
A number of techniques for modeling frequency dependent boundary
conditions in the FDTD method are presented and are validated against the Boundary
Element Method (BEM). The results show that a Z-transform based multi-degree-offreedom
model is the most effective for frequency dependent boundary conditions.
Also of interest is that, when there is enough random incident waves onto the
boundaries in the room, the energy based absorption coefficient can be used in
conjunction with a minimum phase approach to obtain a suitable approximation for
the time domain boundary condition in FDTD calculations.
A thorough analysis on different source implementations is presented, and the
cause of hard source problem is revealed. Based on the findings, a Time Limited Sine
Modulated Gaussian Hard (TLSGH) source is developed that has the same
characteristics of a transparent source, and yet retains the excellent computational
efficiency of a hard source implementation.
For a room with tilted boundary, results in this thesis show that standard FDTD
using stair-case approximation can cause errors that exceed subjective difference
limens in calculating room acoustic parameters. To solve this problem, the locally
conformal boundary modelling method based on Dey-Mittra FDTD is extended for
frequency dependent boundary conditions.
Putting all together, FDTD method with TLSGH source and locally conformal
frequency dependent boundary conditions shows remarkably good agreement
compared to the more precise BEM. It is concluded that the techniques developed in
this investigation significantly improve the effectiveness of FDTD in room acoustic
simulations.

Citation

Jeong, H. Source and boundary conditions in finite difference time domain modelling of room acoustics. (Thesis). Salford : University of Salford

• Thesis Type: Thesis
• Deposit Date: Oct 3, 2012
• Award Date: Jan 1, 2010