Acoustic simulation of cavities with porous materials using an adaptive model order reduction technique

Abstract

Porous materials are often used in the context of passive noise control applications due to their low cost and good sound absorption properties. As the most commonly used predictive tool, the finite element (FE) method is often applied in the design phase to obtain detailed information on the performance of complex vibro-acoustic systems with porous damping treatments. In this case, however, its use inevitably leads to very large, complex-valued and frequency-dependent numerical models, which makes original full-order model evaluation intractable due to time and memory limitations. In this paper, an adaptive model order reduction strategy is presented to reduce the number of degrees of freedom involved in the associated problems such that the required computational cost can be largely alleviated while a desired high accuracy can be achieved in a controllable way. This technique consists of making use of Taylor expansion to the multiple frequency-dependent scalar functions coming from the complex material behavior, and then performing the structure-preserving second-order Arnoldi algorithm based on a robust error indicator to solve the underlying FE model in the frequency domain. A further improvement in terms of the approximation accuracy of the constructed compact reduced-order model is also proposed to incorporate all available moment-matching information. Two widely used model types for porous materials are investigated, i.e. the equivalent fluid description and the Biot theory. Mono-physical poroelastic-poroelastic coupling and multi-physical acoustic-porous coupling are considered in order to demonstrate the simplicity, versatility and efficiency of the approach.