Adaptive, High-Order Finite-Element Method for Convected Acoustics

Abstract

An improved finite element method for predicting sound propagation in non-uniform flows is proposed. Sound waves are described by the linearised potential theory solved in the frequency domain. Solutions are calculated using the p-FEM method with highorder, hierarchic shape functions which results in a drastic improvement in computational efficiency. The memory and time requirements for solving large-scale problems are significantly reduced compared to 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.

Aerodynamic and Aeroacoustic Performance of Tail Rotor Investigation and Modification

“…The highest acoustic frequency that can be solved in a conventional finite element solver with the one order grid is 740 Hz, according to the relationship between the acoustic wavelength that needs to be satisfied and the grid size, as expressed in the equation (6). In this paper, we used the Adaptive Finite Element Method for Resolution (FEMAO) [25]. The solver automatically adjusts the sequence of the local grid according to the frequency of interest and the location of the sound source.…”

A non-overlapping Schwarz domain decomposition method with high-order finite elements for flow acoustics

“…where N ij defines the terms associated with the interface condition. Equations (19) and (20) can be used to eliminate the degrees of freedom φ i in each sub-domain:…”

“…The domain decomposition formulation is discretized using a p-FEM high-order finite element method [19,20]. Each sub-domain Ω i is approximated by a tessellation of non-overlapping elements.…”

“…The use of a variable polynomial order in each element provides a way to address these two issues. The order is defined thanks to an a priori error indicator introduced in [19] and extended in [20] to the linearized potential equation. The error is estimated on a single one-dimensional element based on the local mesh resolution.…”

“…Detailed information concerning this test case are available in Prinn [24] and Mustafi [28]. This geometry was previously used to benchmark the performance of the a priori p-adaptive strategy for flow acoustics in [20,29].…”