Comparative study of models of impedance boundary conditions in acoustic problems

In this paper, different implementations of numerical locally reacting boundary conditions are studied for acoustic problems. In this comparative study we analyze two types of equations, the Euler equations and the wave equation. We also analyze both finite-differences time-domain (FDTD) algorithms, and pseudo-spectral time domain (PSTD) numerical schemes. We compare different numerical implementations existing in the literature by means of exhaustive numerical experiments. These numerical experiments allow for the study of the absorbing properties of the different schemes as a function of the frequency and the angle of the incident sound waves. This novel comparative study will help the acoustic engineer in order to choose the proper numerical scheme for his/her simulations