Semi-empirical boundary conditions for the linearized acoustic Euler equations using Pseudo-Spectral Time-Domain methods

Abstract

Pseudo-Spectral Time-Domain algorithms have emerged as new numerical methods for solving Eulerian problems. These methods, in contrast to more common finite-difference, time-domain approaches, provide isotropic dispersion characteristics. However, the technical literature concerning to this topic presents a serious lack of methods for dealing with partially reflecting boundary conditions in order to simulate surfaces of a specified impedance. In the current paper we present a novel semi-empirical formulation for simulating constant impedance boundary conditions within Pseudo-Spectral techniques based on the Fourier transform. Finally, the validations in one and two dimensions by means of different numerical experiments, show the accuracy of the model.