Computational modeling of broadband acoustic fields in enclosures with specular reflection boundaries using a first-principles energy method

Abstract

Steady-state sound fields in enclosures with specular reflection boundaries are modeled with a first-principle energy-intensity boundary element method using uncorrelated broadband directional sources. The specular reflection field is represented by a limited set of spherical harmonics, orthogonal on the half-space. For each boundary element, the amplitudes of these harmonics are determined from the incident field from all other elements and sources, and are subject to an energy conservation integral constraint using a Lagrange multiplier method. The computational problem is solved using an iterative relaxation method starting from the 3-D diffuse reflection solution. At each iteration, directivity harmonics are estimated by post-processing and the influence matrix is refined accordingly. For internal sources, simple first reflection images improve accuracy with virtually no penalty on computation time. Convergence occurs in relatively few relaxation steps. Extrapolating to an infinite number of boundary elements and iterations gives very accurate results. Results are compared to exact benchmark solutions obtained from a frequency-by-frequency modal analysis, and to a broadband image method. The method of absorption scaling is verified for 3-D cases, and showing that the spatial variation in rooms is largely determined by source position and the relative distribution of absorption, but not the overall absorption level.