Finite Element based methods are of interest when the analytical solution for a waveguide cross section is not available. In this work, efforts are made towards the reduction of the Finite Element models size for duct acoustics. The Galerkin Finite Element formulation is used for a local elementary modelling of a uniform duct with mean flow. For the slowly varying cross section ducts, wavenumbers are found locally by means of an eigenvalue problem and the net change of amplitudes between two points along a propagation axis provides finally, through conservation of the time-averaged energy, the solutions for the propagating waves. Although this does not take into consideration the eventual reflection throughout the varying cross section part, it can be used when the cross section variation is slow and its analytical solution is not available. Should speed in the first place be sought, the approach is satisfactory when models are important in size. Accuracy and speed of the approach are discussed while comparing versus an actual full Finite Element modelling.

当波导横截面的解析解不可用时，基于有限元的方法是有用的。在这项工作中，努力减少管道声学的有限元模型尺寸。Galerkin 有限元公式用于对具有平均流的均匀管道进行局部基本建模。对于缓慢变化的横截面管道，波数是通过特征值问题局部找到的，沿着传播轴的两点之间的净振幅变化最终通过时间平均能量守恒提供了传播波的解。虽然这没有考虑到整个变化横截面部分的最终反射，但可以在横截面变化缓慢且其解析解不可用时使用。如果首先要寻求速度，那么当模型的大小很重要时，这种方法是令人满意的。在与实际的完整有限元建模进行比较时，讨论了该方法的准确性和速度。