Modelling high-frequency waves using the Radiative Transfer Equation: A Discontinuous Galerkin Approach

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.