Application of adaptive polynomial finite element method to predict wide-frequency acoustic behavior of silencer

The adaptive polynomial finite element method (p-FEM) is applied to efficiently predict the wide-frequency acoustic attenuation performance of silencers using a single mesh. A priori, an edge-driven adaptive strategy is developed to account for influences of the acoustic properties of porous material described by equivalent fluid models on element orders. The treatment details of boundary integrals on perforations, inlet, and outlet are discussed, and expressions are formulated to determine the transmission loss of the silencer with consideration of three-dimensional wave effects in inlet and outlet ducts. The computational process and implementation in codes for p-FEM are introduced in detail. The p-FEM with the present adaptive strategy is applied to predict the transmission loss of silencers, and good agreements between predictions and measurements, as well as benchmark data calculated by other methods, validate the presented approach. For large silencers discretized by the tetrahedral and hexahedral elements, the computation speed of p-FEM is 4.4 and 15 times that of the Galerkin/least squares finite element method, respectively. Effects of the acoustic properties of porous material on the element order, as well as impacts of high-order modal incidences and mean flow on the acoustic attenuation behavior of a large silencer are discussed.