In aeroacoustics applications, such as turbo machines and turbofan aircraft engines, the problems are often posed on large or unbounded domains. Several numerical methods have been used to solve these problems: The Finite Difference Method (FDM), the Finite Element Method (FEM) or Finite Volume Method (FVM). Numerical methods need efficient and easy to implement techniques to truncate the computational domain without disturbing the solution of the original problem. Several methods have been developed in the literature to cope with unbounded domain problem : the Non-Reflecting Boundary Condition (NRBC) methods using the operator commonly called Dirichlet-to-Neumann (DtN) based on an analytical representation of the external field and needing particular geometries, Infinite Element Methods (IEM) whose efficiency depends on the choice of the multipole expansion functions in the radial direction and on the truncation of the radial order or Perfectly Matched Layer (PML) method who simulates an absorbing layer surrounding the computational domain. This last method has become very popular in recent years, given the ease of integration into a computational code.

In this review, we will try to expose the different aspects that govern the development of this method, the difficulties it can present and the different solutions proposed in the literature.

Mabrouk Ben Tahar is emeritus Professor, the University of Technology of Compiègne – France. He holds a Ph.D. degree (1981) and Doctor of Science (docteur ès-sciences) (1991) from the University of Technology of Compiègne. He was appointed to the University of Technology of Compiègne in 1982, an associate professor from 1988-1999 and from 2000-2022 was a full professor (Classe Exceptionnelle) in the mechanical engineering department. He also served as a Head of the Acoustic group (2000-2017) and a Head of the doctoral school in mechanical engineering.

He is a Fellow of the French Society of Acoustic (SFA) and the French Mechanical Association (AFM). He was a visiting/researcher/professor at the Institute of Sound and Vibration (ISVR), Laval University Quebec-Canada, Technical University of Denmark, the Sherbrook University Canada, the Institute of Vibration, Shock & Noise, the Shanghai Jiao Tong University, Mohammadia Engineering School, the Mohammed V University, Rabat-Morocco, Engineering School of Monastir-Tunisia, Engineering School of Gabès-Tunisia and Engineering School of Adelaide university.

His primary research focuses on the numerical methods in acoustic and aeroacoustics (CAA). The major focus has been the numerical approach of aeroacoustics using Galbrun’s equation. He has supervised more than twenty Ph.D. students, published more than 40 scientific articles, and more than 100 international and national conferences.