Time-domain prediction of acoustics in domains with realistic boundaries

Abstract

The validity of the recently proposed time-domain impedance boundary condition is explored. The one-dimensional piston in an impedance tube problem is formulated and attempted using the classical Laplace transform to compare with a recently developed time-domain method. It will be shown that the classical frequency-domain method does not lead to uniformly convergent analytic solutions in one-dimension, but to finite series approximations, which resemble the long time stable and accurate numerical solutions. The time-domain solution with time-domain impedance boundary condition is then compared with the frequency-domain solution of harmonic point sources near an impedance plane in two dimensions, which establishes the agreement between time-domain and frequency-domain approaches at discrete frequencies. Solutions for noise abatement with mixed impedance grounds using different mixed impedance models and Boundary Element Method (BEM) numerical scheme are compared with those using the time-domain approach. Applications and further extensions of the time-domain approach to problems in acoustics will be addressed.