Modelling high-frequency waves using the radiative transfer equation: a discontinuous Galerkin approach

Lockett, R ORCID: https://orcid.org/0009-0003-8463-4325 and Chappell, D ORCID: https://orcid.org/0000-0001-5819-0271, 2025. Modelling high-frequency waves using the radiative transfer equation: a discontinuous Galerkin approach. In: Proceedings of the 54th International Congress and Exposition on Noise Control Engineering. Recife, Brazil: Even3. ISBN 9786527215738

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Abstract

The effective modelling of high-frequency waves is critical to accurately describing noise generation and control in a broad range of engineering applications. We will explain the connection between high-frequency asymptotic solutions to frequency domain wave equations and the radiative transfer equation (RTE) via a kinetic formulation of the classical Hamiltonian ray dynamics. The numerical solution of the arising RTE requires a discretisation in both the position and direction coordinates. We will introduce a computational framework based on the Discontinuous Galerkin method in space and compare the commonly used discrete ordinate method in direction with a Fourier-based approach. This work builds on previous research into high-frequency vibroacoustic simulation methods, having the same advantages as Dynamical Energy Analysis (DEA), which offers higher precision than the more established Statistical Energy Analysis. The RTE approach adopted here is beneficial since it uses a more familiar finite element based methodology and the degree of the local spatial polynomial approximation can be increased more simply and at lower computational cost than in DEA. We then discuss future work to extend our approach for analysing complex built-up structures, incorporating multi-material modelling and the subsequent wave interactions such as refraction and reflection at the inter-element boundaries.

Item Type:	Chapter in book
Alternative Title:	Modelling high-frequency waves using the radiative transfer equation
Description:	Paper presented at the 54th International Congress and Exposition on Noise Control Engineering (Inter-Noise 2025), 24-27 August 2025, São Paulo, Brazil.
Creators:	Lockett, R. and Chappell, D.
Publisher:	Even3
Place of Publication:	Recife, Brazil
Date:	25 September 2025
ISBN:	9786527215738
Identifiers:	Number Type 2507253 Other
Rights:	Permission is granted for the reproduction of a fractional part of this paper published in the Proceedings of INTER-NOISE 2025 provided permission is obtained from the author(s) and credit is given to the author(s) and these proceedings.
Divisions:	Schools > School of Science and Technology
Record created by:	Jonathan Gallacher
Date Added:	14 Oct 2025 13:06
Last Modified:	14 Oct 2025 13:06
URI:	https://irep.ntu.ac.uk/id/eprint/54564

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