3D isogeometric indirect BEM solution based on virtual surface sources on the boundaries of Helmholtz acoustic problems

Shaaban, Ahmed Mostafa; Trevelyan, Jon; Rabczuk, Timon

Abstract

A solution for 3D Helmholtz acoustic problems is introduced based on an indirect boundary element method (indirect BEM) coupled with isogeometric analysis (IGA). The novelty of this work arises from using virtual surface sources placed directly on the scatterer boundaries, producing robust results. These virtual surface sources are discretized by the same Non-Uniform Rational B-Splines (NURBS) approximating the scatterer CAD model. This allows modelling of general irregular geometries. The proposed solution has the same features of BEM approaches, which do not need any domain discretization or truncation boundaries at the far-field. It shows an additional merit by arranging the linear system of equations directly depending on a single coefficient matrix, consuming less computational time compared to other BEM methods. A Greville abscissae collocation scheme is proposed with offsets at C0-continuities. This collocation scheme allows for easy evaluation for both free-terms and normals at the collocation points.

The performance of the proposed solution is discussed on 3D numerical exterior problems and compared against other BEM methods. Then, the practical interior muffler problem with internal extended thin tubes is studied and the obtained results are compared against other numerical methods in addition to the available experimental data, showing the capability of the proposed solution in handling thin-walled geometries.

Citation

Shaaban, A. M., Trevelyan, J., & Rabczuk, T. (2024). 3D isogeometric indirect BEM solution based on virtual surface sources on the boundaries of Helmholtz acoustic problems. Engineering with Computers, https://doi.org/10.1007/s00366-023-01933-5

• Journal Article Type: Article
• Acceptance Date: Dec 1, 2023
• Online Publication Date: Feb 6, 2024
• Publication Date: Feb 6, 2024
• Deposit Date: Feb 7, 2024
• Publicly Available Date: Feb 8, 2024
• Journal: Engineering with Computers
• Print ISSN: 0177-0667
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1007/s00366-023-01933-5
• Keywords: 3D, Acoustics, Indirect BEM, Collocation, IGA
• Public URL: https://durham-repository.worktribe.com/output/2228900