Higher order finite element modeling of acoustic propagation in a moving medium

This research considers the finite element modeling of the convective potential formulation of acoustic propagation and radiation. Higher order elements have been used to increase the computational efficiency of duct and turbofan models. Cubic serendipity elements have been implemented in a non-uniform duct model of acoustic propagation in a moving medium. These elements outperform the quadratic serendipity elements in terms of reducing the dimensionality without losing accuracy based on visual observations and error norm analysis. Comparisons show that for computation of acoustic pressure the cubic element formulation converges at a higher rate than the quadratic. CPU time reduction of up to 40% has been observed without sacrifice in accuracy. Serendipity elements have also been compared in performance to Lagrangian elements. Any penalty in numerical accuracy incurred by using serendipity elements rather than Lagrangian elements is far outweighed by the gains in dimensionality. Analytical expressions for the effects of convection and that of acoustic propagating modes on the wavelength have been formulated and compared to numerical results. The cubic serendipity elements have also been applied to the near field of inlet and aft acoustic radiation models for a turbofan engine resulting in considerable reduction in the dimensionality of the problem without sacrificing accuracy. Preliminary assessment of alternative finite element approaches to model the convective potential formulation has been conducted. Stabilization and wave approximation methods have been implemented to solve simple one-dimensional problems.