Efficient solutions of preconditioned large‐scale systems for simulative aircraft cabin noise assessment

Abstract

The rising number of passengers transported by aircraft leads to more flight traffic, further increasing the environmental impact of the aviation sector. In order to combat the growing environmental impact, the Cluster of Excellence Sustainable and Energy Efficient Aviation of TU Braunschweig aims to advance research toward climate neutral aviation, especially with the design of newly developed aircraft. In the conscience of passengers, the focus is also shifted toward a healthy and comfortable travel experience. One of the main factors influencing these aspects is noise inside the aircraft cabin. A lower noise impact can help increase the technology acceptance and further push toward more sustainable airborne transport solutions. In order to assess cabin noise with moderate effort in an early design stage, simulative methods such as the finite element method (FEM) are deployed. These have the advantage of yielding important insights into the noise distribution inside the aircraft cabin without having to have a built prototype present. Since methods like the FEM are of a wave‐resolving nature, results contain high‐resolution wave propagation information of the sound waves, created, for example, by the excitation of the turbulent boundary layer on the aircraft's outer skin. Additionally, a direct auralization at seat positions is possible. More powerful computers have further improved the usage of models for an early design noise assessment. However, the more elaborate a model is, the more degrees of freedom (DOFs) it yields as final system of equations. Finally, since the FEM is of wave‐resolving nature and in order to depict sound waves accurately, a fine discretization of 10 nodes per frequency dependent wave length is needed. This leads to a massive increase in DOFs for higher frequencies and finally yielding a large‐scale model, which entails huge computational efforts. This makes the usage of adaptive grids very convenient. In this contribution, adaptive grids entail two main aspects: frequency and domain adaptive discretization. Since higher frequencies lead to shorter wavelengths and therefore finer mesh sizes, it is feasible to adaptively discretize the model in the frequency domain, while also adaptively discretizing the different domains of the models itself, because different materials lead to different wavelengths. However, the resulting system of equations might be ill‐posed. Therefore, this contribution aims to shed light on an efficient solving process of these adaptively discretized large‐scale models with preconditioning and adequate solver choice.