| Practical problems concerning the aeroacoustics of aircraft demand the use of unstructured grids, to handle the complex geometry boundaries. The work presented in this thesis develops, implements and optimizes high order accurate algorithms on unstructured grids using Finite Element Methods. The focus of the applications is on problems involving the propagation of sound in sheared mean flows. Methods are developed for both time and frequency domain solutions of the linearized Euler equations in two spatial dimensions. In the time domain, a solver using the Discontinuous Galerkin method is developed. A novel way to approximate the flux expressions in the linearized Euler equations is implemented. This reduces the computational cost considerably relative to existing Discontinuous Galerkin implementations. The two dimensional solver is designed to run on parallel computing platforms, and is validated by solving several benchmark problems. The parallel Discontinuous Galerkin solver is then used to simulate the acoustic propagation in the shear layer of a realistic aircraft jet engine exhaust configuration, modeled as a rectangular nozzle. In the frequency domain, the suppression of the instability wave solution of the linearized Euler equations is sought on unstructured grids. The implementation and evaluation of the Discontinuous Galerkin method for frequency domain applications is carried out. A continuous, Streamline Upwind Petrov Galerkin method is then used to obtain only the acoustic solution for a benchmark problem involving the instability waves in two dimensions. Unlike other existing frequency domain solvers, no assumption is made regarding the nature of the mean flow. This feature assures that the methods developed in this study are better suited for problems of practical interest. |
