Numerical methods for acoustics and noise control

Abstract

This dissertation considers numerical methods for wave propagation modelling and noise control. The first part of the dissertation discusses an efficient method for solving time-harmonic wave equations in acoustic (the Helmholtz equation) and elastic domains (the Navier equation). The solver is based on preconditioning a Krylov subspace method, such as GMRES, with approximations of damped variants of the corresponding wave equations. An algebraic multigrid method is used in approximating the inverse of damped operators. The method can be used in complex three-dimensional computational domains with varying material properties. The second part of the dissertation considers noise control problems. Two different noise control problems are discussed in detail. First, a shape optimization of a duct system with respect to sound transmission loss is discussed. The sound transmission loss is maximized at multiple frequency ranges simultaneously, by adjusting the shape of a reactive muffler component. The noise reduction problem is formulated as a multiobjective optimization problem for the NSGA-II genetic algorithm. The discussed method provides an efficient approach to design muffler components. Second, a novel method is introduced for assessing the effectiveness of the optimal anti-noise for local sound control in a stochastic domain. A three-dimensional enclosed acoustic space, for example, a cabin with acoustic actuators in given locations, is modelled using the finite element method in the frequency domain. In a model problem, a significant noise reduction is demonstrated particularly at lower frequencies.