Simulating time-harmonic acoustic wave effects induced by periodic holes/inclusions on surfaces

TL;DR

This paper presents a novel localized meshless method using the generalized finite difference approach to simulate time-harmonic acoustic waves on curved surfaces with periodic holes, improving accuracy and efficiency.

Contribution

It introduces the first localized meshless technique employing the generalized finite difference method for acoustic wave analysis on complex curved surfaces with periodic inclusions.

Findings

Accurately simulates wave propagation on complex geometries.

Reduces boundary reflections with an absorbing boundary condition.

Demonstrates efficiency and accuracy through benchmark examples.

Abstract

This paper introduces the first attempt to employ a localized meshless method to analyze time-harmonic acoustic wave propagation on curved surfaces with periodic holes/inclusions. In particular, the generalized finite difference method is used as a localized meshless technique to discretize the surface gradient and Laplace-Beltrami operators defined extrinsically in the governing equations. An absorbing boundary condition is introduced to reduce reflections from boundaries and accurately simulate wave propagation on unclosed surfaces with periodic inclusions. Several benchmark examples demonstrate the efficiency and accuracy of the proposed method in simulating acoustic wave propagation on surfaces with diverse geometries, including complex shapes and periodic holes or inclusions.