Stable Perfectly Matched Layers with Lorentz transformation for the convected Helmholtz equation

International audiencePerfectly Matched Layers (PMLs) appear as a popular alternative to non-reflecting boundary conditions for wave-type problems. The core idea is to extend the computational domain by a fictitious layer with specific absorption properties such that the wave amplitude decays significantly and does not produce back reflections. In the context of convected acoustics, it is well-known that PMLs are exposed to stability issues in the frequency and time domain. It is caused by a mismatch between the phase velocity on which the PML acts, and the group velocity which carries the energy of the wave. The objective of this study is to take advantage of the Lorentz transformation in order to design stable perfectly matched layers for generally shaped convex domains in a uniform mean flow of arbitrary orientation. We aim at presenting a pedagogical approach to tackle the stability issue. The robustness of the approach is also demonstrated through several two-dimensional high-order finite element simulations of increasing complexity

A new construction of perfectly matched layers for the linearized Euler equations

Based on a PML for the advective wave equation, we propose two PML models for the linearized Euler equations. The derivation of the first model can be applied to other physical models. The second model was implemented. Numerical results are shown.Comment: submitted for publication on February 1st 2005 What's new: interface conditions for the first PML model, a 3D section, more numerical result

Efficient finite element methods for aircraft engine noise prediction

Aircraft noise has a negative environmental impact. One of the ways in which it can be mitigated is by placing acoustic liners inside the aircraft's engines. These liners can be optimised for noise reduction. A cost effective way to optimise acoustic liners is to make use of numerical modelling. However, there is room for improvement of the efficiency of current modelling methods. This thesis is concerned with the efficient numerical prediction of noise emitted from modern aircraft engines. Four high order finite element methods are used to solve the convected wave equation, and their performances are compared. The benefit of using the hierarchic Lobatto finite element method to solve this type of problem is demonstrated. A scheme which optimises the efficiency of the high order method is developed. The scheme automatically chooses the most efficient order for a given element, depending on the element size, and the problem parameters on that element. The computational cost of using the standard quadratic finite element method to solve a typical engine intake noise problem, is compared to the cost of the proposed adaptive-order method. A significant improvement in terms of efficiency is demonstrated when using the proposed method over the standard method. Furthermore, a new formulation based on potential flow theory for the solution of vortex sheet problems (typically encountered when dealing with exhaust noise problems) is presented.