Finite element modeling of acoustics using higher order elements. Part I: Nonuniform duct propagation

摘要

Cubic serendipity elements have been implemented into a nonuniform duct model of acoustic propagation in a moving medium. This model uses a convective potential formulation derived from the inviscid linearized mass and momentum equations. The model requires post-processing to calculate acoustic pressure. These elements outperform the quadratic serendipity elements in terms of computational efficiency based on visual observations and error norm analysis of acoustic pressure. CPU time reduction of up to 40% has been observed without sacrificing accuracy. Any penalty in numerical accuracy incurred by using serendipity elements rather than Lagrangian elements is far outweighed by the gains in dimensionality. The computational gains for calculation of acoustic potential are considerably less. Analytical expressions for the modal and convective effects on the propagating wavelength have been formulated and compared to numerical results. 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.