Adaptive, high-order finite-element method for convected acoustics

An improved finite-element method for predicting sound propagation in nonuniform flows is proposed. Sound waves are described by the linearized potential theory solved in the frequency domain. Solutions are calculated using the p-FEM method with high-order, hierarchic shape functions that results in a drastic improvement in computational efficiency. The memory and time requirements for solving large-scale problems are significantly reduced compared with standard finite-element methods. An additional feature presented in this paper is an adaptive scheme to select the optimal interpolation order in each element so as to achieve a prescribed accuracy. This greatly simplifies the preparation of the numerical model. When performing a series of calculations at different frequencies there is no need to adjust the mesh to maintain a sufficient resolution. Instead the adaptive p-FEM method adjusts the interpolation order automatically to ensure an accurate solution is obtained. The performance of the method is demonstrated for three-dimensional test cases for noise radiation from a turbofan intake. Guidelines for preparing models using this adaptive, high-order approach are also discussed.