Diffraction of acoustic waves by a wedge of point scatterers

TL;DR

This paper develops an efficient numerical method to analyze acoustic wave diffraction by a wedge made of two semi-infinite periodic arrays of point scatterers, enabling accurate computation of complex interactions.

Contribution

It introduces a novel iterative Wiener--Hopf based approach with effective series truncation for modeling diffraction by scatterer wedges.

Findings

Method accurately predicts diffraction patterns.

Converges for a wide range of physical cases.

Validated against direct numerical simulations.

Abstract

This article considers the problem of diffraction by a wedge consisting of two semi-infinite periodic arrays of point scatterers. The solution is obtained in terms of two coupled systems, each of which is solved using the discrete Wiener--Hopf technique. An effective and accurate iterative numerical procedure is developed to solve the diffraction problem, which allows us to compute the interaction of thousands of scatterers forming the wedge. A crucial aspect of this numerical procedure is the effective truncation of slowly convergent single and double infinite series, which requires careful asymptotic analysis. A convergence criteria is formulated and shown to be satisfied for a large class of physically interesting cases. A comparison to direct numerical simulations is made, highlighting the accuracy of the method.