An automatic perfectly matched layer for acoustic finite element simulations in convex domains of general shape

Abstract

This article addresses the efficient finite element solution of exterior acoustic problems with truncated computational domains surrounded by perfectly matched layers (PMLs). The PML is a popular nonreflecting technique that combines accuracy, computational efficiency, and geometric flexibility. Unfortunately, the effective implementation of the PML for convex domains of general shape is tricky because of the geometric parameters that are required to define the PML medium. In this work, a comprehensive implementation strategy is proposed. This approach, which we call the automatically matched layer (AML) implementation, is versatile and fully automatic for the end-user. With the AML approach, the mesh of the layer is extruded, the required geometric parameters are automatically obtained during the extrusion step, and the practical implementation relies on a simple modification of the Jacobian matrix in the elementwise integrals. The AML implementation is validated and compared with other implementation strategies using numerical benchmarks in two and three dimensions, considering computational domains with regular and nonregular boundaries. A three-dimensional application with a generally shaped domain generated using a convex hull is proposed to illustrate the interest of the AML approach for realistic industrial cases. K E Y W O R D S exterior acoustics, finite element method, Helmholtz equation, perfectly matched layer, wave propagation 1 INTRODUCTION Finite element methods (FEMs) are widely used in academia and industry to simulate acoustic wave propagation phenomena. With these methods, high-frequency oscillatory fields can be represented accurately in realistic settings with complicated geometries thanks to unstructured meshes, curved elements, high-order basis functions and hp-adaptivity. 1 Nevertheless, for many applications occurring in the free space, the computational domain must be truncated, and a specific nonreflecting technique must be used at the artificial boundary of the finite element mesh to represent the outward [Correction added on 6 January 2021, after first online publication: ζ symbols have been corrected to throughout the article.] This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Trailing-Edge Noise Prediction by Solving Helmholtz Equation with Stochastic Source Term

“…We use here the locally-conformal implementation described in [39]. The latter is equipped with the parameter-free unbounded absorbing function from [40].…”

“…3). This domain is surrounded by a ten-layer PML region to absorb the outgoing waves [39]. An unstructured triangular mesh characterized by a constant element size ℎ ac = 0.1ℓ is designed using the open source mesh generator Gmsh [53].…”

Measurement and modelling of aero-acoustic installation effects in tractor and pusher propeller architectures

“…The {ATV} is now a matrix composed of the ATVs for each observer and acoustic mesh points. They have been computed using the FEM solver of the Simcenter 3D simulation platform [45], featuring Adaptative Order finite elements (FEM-AO, [50,51]) and Automatic Matched Layers (AML, [52]) for non-reflective boundary conditions.…”

“…One of the outcomes of this research is the numerical strategy based on BEM described and used in this paper. As a complement, VKI has used the FEM solver of the Simcenter 3D simulation platform developed by Siemens [45], featuring Adaptative Order finite elements (FEM-AO, [50,51]) and Automatic Matched Layers (AML, [52]) for non-reflective boundary conditions. Such conditions are prescribed in the present study based on the assumption that acoustic waves propagating away from the test section are damped out and not re-injected through the closed loop wind tunnel.…”

Aerodynamic and Aeroacoustic Performance of Tail Rotor Investigation and Modification

“…Due to the existence of complex structures such as blades, hub covers, and sidewalls on the inner surface of the duct, the automatic pairing layer (AML) is used as the radiation boundary of the external infinite far field when calculating the radiation from the sound source to the outside. At the same time, the finite grid limit causing acoustic pseudo-reflection is avoided [24]. The reflections and diffuser of arbitrary geometrical shapes can be taken into account so that the calculation allows to separate the intrinsic interference characteristics of the source and the presence of the shroud.…”