Use of finite element methods in frequency domain aeroacoustics

The linearized Euler equations are used widely in many aerodynamic noise prediction schemes. The linearized Euler equations also support instability waves, which can obscure the acoustic solution. An approach to suppress the instability waves is to solve the linearized Euler equations in the frequency domain. Also, the frequency domain approach is far less expensive compared to the time domain approach in terms of the computational time though only a single frequency can be computed at one time. The application and comparison of two unstructured grid methods for the solution of aeroacoustic problems in the frequency domain are presented. Algorithms are developed using the discontinuous Galerkin and the streamline upwind Petrov-Galerkin finite element methods in two spatial dimensions on conforming triangular meshes using nodal polynomial basis sets. Unlike other existing frequency domain solvers, no assumption is made regarding the nature of the mean flow. The application of the two methods to a two-dimensional benchmark problem involving the suppression of instability waves is presented. The two methods are compared in terms of the computational cost. It is concluded that the discontinuous Galerkin method is prohibitively more expensive compared to the streamline upwind Petrov-Galerkin method for aeroacoustic applications in the frequency domain using conforming meshes and nodal polynomials.