Room acoustics modelling in the time-domain with the nodal discontinuous Galerkin method

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Abstract

To solve the linear acoustic equations for room acoustic purposes, the performance of the time-domain nodal discontinuous Galerkin (DG) method is evaluated. A nodal DG method is used for the evaluation of the spatial derivatives, and for the time-integration an explicit multi-stage Runge-Kutta method is adopted. The scheme supports a high order approximation on unstructured meshes. To model frequency-independent real-valued impedance boundary conditions, a formulation based on the plane wave reflection coefficient is proposed. Semi-discrete stability of the scheme is analyzed using the energy method. The performance of the DG method is evaluated for four three-dimensional configurations. The first two cases concern sound propagations in free field and over a flat impedance ground surface. Results show that the solution converges with increasing DG polynomial order and the accuracy of the impedance boundary condition is independent on the incidence angle. The third configuration is a cuboid room with rigid boundaries, for which an analytical solution serves as the reference solution. Finally, DG results for a real room scenario are compared with experimental results. For both room scenarios, results show good agreements.
LanguageEnglish
Pages2650–2663
Number of pages14
JournalJournal of the Acoustical Society of America
Volume145
Issue number4
DOIs
StatePublished - 30 Apr 2019

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Galerkin method
rooms
acoustics
impedance
boundary conditions
Runge-Kutta method
energy methods
wave reflection
sound propagation
configurations
mesh
polynomials
plane waves
incidence
reflectance
formulations
Modeling
Acoustics
evaluation
approximation

Bibliographical note

Copyright (2019) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.

Cite this

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title = "Room acoustics modelling in the time-domain with the nodal discontinuous Galerkin method",
abstract = "To solve the linear acoustic equations for room acoustic purposes, the performance of the time-domain nodal discontinuous Galerkin (DG) method is evaluated. A nodal DG method is used for the evaluation of the spatial derivatives, and for the time-integration an explicit multi-stage Runge-Kutta method is adopted. The scheme supports a high order approximation on unstructured meshes. To model frequency-independent real-valued impedance boundary conditions, a formulation based on the plane wave reflection coefficient is proposed. Semi-discrete stability of the scheme is analyzed using the energy method. The performance of the DG method is evaluated for four three-dimensional configurations. The first two cases concern sound propagations in free field and over a flat impedance ground surface. Results show that the solution converges with increasing DG polynomial order and the accuracy of the impedance boundary condition is independent on the incidence angle. The third configuration is a cuboid room with rigid boundaries, for which an analytical solution serves as the reference solution. Finally, DG results for a real room scenario are compared with experimental results. For both room scenarios, results show good agreements.",
author = "Huiqing Wang and Indra Sihar and {Pagan Munoz}, Raul and Maarten Hornikx",
note = "Copyright (2019) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.",
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AU - Wang,Huiqing

AU - Sihar,Indra

AU - Pagan Munoz,Raul

AU - Hornikx,Maarten

N1 - Copyright (2019) Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.

PY - 2019/4/30

Y1 - 2019/4/30

N2 - To solve the linear acoustic equations for room acoustic purposes, the performance of the time-domain nodal discontinuous Galerkin (DG) method is evaluated. A nodal DG method is used for the evaluation of the spatial derivatives, and for the time-integration an explicit multi-stage Runge-Kutta method is adopted. The scheme supports a high order approximation on unstructured meshes. To model frequency-independent real-valued impedance boundary conditions, a formulation based on the plane wave reflection coefficient is proposed. Semi-discrete stability of the scheme is analyzed using the energy method. The performance of the DG method is evaluated for four three-dimensional configurations. The first two cases concern sound propagations in free field and over a flat impedance ground surface. Results show that the solution converges with increasing DG polynomial order and the accuracy of the impedance boundary condition is independent on the incidence angle. The third configuration is a cuboid room with rigid boundaries, for which an analytical solution serves as the reference solution. Finally, DG results for a real room scenario are compared with experimental results. For both room scenarios, results show good agreements.

AB - To solve the linear acoustic equations for room acoustic purposes, the performance of the time-domain nodal discontinuous Galerkin (DG) method is evaluated. A nodal DG method is used for the evaluation of the spatial derivatives, and for the time-integration an explicit multi-stage Runge-Kutta method is adopted. The scheme supports a high order approximation on unstructured meshes. To model frequency-independent real-valued impedance boundary conditions, a formulation based on the plane wave reflection coefficient is proposed. Semi-discrete stability of the scheme is analyzed using the energy method. The performance of the DG method is evaluated for four three-dimensional configurations. The first two cases concern sound propagations in free field and over a flat impedance ground surface. Results show that the solution converges with increasing DG polynomial order and the accuracy of the impedance boundary condition is independent on the incidence angle. The third configuration is a cuboid room with rigid boundaries, for which an analytical solution serves as the reference solution. Finally, DG results for a real room scenario are compared with experimental results. For both room scenarios, results show good agreements.

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