Time Domain Room Acoustic Solver with Fourth-Order Explicit FEM Using Modified Time Integration

Takumi Yoshida,Takeshi Okuzono,Kimihiro Sakagami

doi:10.3390/app10113750

Abstract

This paper presents a proposal of a time domain room acoustic solver using novel fourth-order accurate explicit time domain finite element method (TD-FEM), with demonstration of its applicability for practical room acoustic problems. Although time domain wave acoustic methods have been extremely attractive in recent years as room acoustic design tools, a computationally efficient solver is demanded to reduce their overly large computational costs for practical applications. Earlier, the authors proposed an efficient room acoustic solver using explicit TD-FEM having fourth-order accuracy in both space and time using low-order discretization techniques. Nevertheless, this conventional method only achieves fourth-order accuracy in time when using only square or cubic elements. That achievement markedly impairs the benefits of FEM with geometrical flexibility. As described herein, that difficulty is solved by construction of a specially designed time-integration method for time discretization. The proposed method can use irregularly shaped elements while maintaining fourth-order accuracy in time without additional computational complexity compared to the conventional method. The dispersion and dissipation characteristics of the proposed method are examined respectively both theoretically and numerically. Moreover, the practicality of the method for solving room acoustic problems at kilohertz frequencies is presented via two numerical examples of acoustic simulations in a rectangular sound field including complex sound diffusers and in a complexly shaped concert hall.

Highlights

IntroductionIt is crucially important to predict accurate impulse responses to provide comfortable acoustic environments necessary for various rooms such as concert halls, offices, and classrooms
We demonstrate the performance of the proposed explicit time domain finite element method (TD-FEM) using a modified Adams method via two room acoustic problems at kilohertz frequencies in a large rectangular room including complicated sound diffusers, and in a concert hall with two conditions
Regarding the advantage of using explicit TD-FEM, it can simulate sound propagation in concert halls, with approximately one-fifth less computational time than that of the implicit standard TD-FEM and one-third times the fourth-order accurate implicit TD-FEM used for reference calculation. These results suggest the high efficiency of the proposed explicit TD-FEM for acoustic simulations in complicated sound fields at kilohertz frequencies

Summary

Introduction

It is crucially important to predict accurate impulse responses to provide comfortable acoustic environments necessary for various rooms such as concert halls, offices, and classrooms. One can design room acoustics via visualization and auralization of sound fields as well as calculating room acoustic parameters such as reverberation times and the speech transmission index. Computer simulation methods are indispensable tools for room acoustic modeling because they can virtually simulate acoustics in architectural spaces. Simulation can facilitate parametric studies more readily than scale model experiments for designing basic room shapes and interior finishes that is, selection of acoustical absorptive or reflective materials [1]. Geometrical acoustics simulation methods have flourished since their original

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