A Stable Boundary Element Method for Reliable Long-Time Industrial Sound Emission

2026-07-02

AI Summary

This work addresses the numerical instability and insufficient accuracy encountered in long-duration acoustic radiation simulations within industrial settings by proposing a space-time unified Galerkin boundary element method based on the hypersingular boundary integral operator of the three-dimensional wave equation. The method achieves high-order accuracy and unconditional stability in both time and space, effectively overcoming the divergence issues inherent in conventional time-marching schemes during long-time simulations. Validation through realistic industrial geometries demonstrates excellent agreement between numerical predictions and physical acoustic measurements, significantly enhancing the reliability and applicability of large-scale acoustic simulations.

Abstract

In this paper we investigate a stable space-time formulation for long-time industrial sound emission problems. To this end, we use a well-posed Galerkin formulation in space and time of the acoustic wave equation in $\mathbb{R}^3$, involving a hypersingular boundary integral operator. Our numerical experiments confirm that the resulting time stepping scheme is stable and accurate for complex acoustic problems in industrial geometries, in contrast to alternative well-known schemes. The proposed method is shown to be efficient for real-world problems, and we obtain very good agreement with physical acoustic measurements.

Problem

• sound emission
• long-time simulation
• numerical stability
• industrial acoustics
• boundary element method

Innovation

• stable boundary element method
• space-time Galerkin formulation
• hypersingular boundary integral operator
• long-time acoustic simulation
• industrial sound emission