A Boundary Node Method for Solving Interior and Exterior Acoustic Problems

IF 1.4 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

International Journal of Computational Methods Pub Date : 2024-02-27 DOI:10.1142/s021987622350041x

Mohammed Afzal Rafiq, I. R. Praveen Krishna, C. O. Arun

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引用次数: 0

Abstract

The Boundary Node Method (BNM) is a meshfree scheme for solving Boundary Integral Equations (BIE). BNM simplifies the problem at two levels. Primarily, as BNM aims to solve the integral form of the governing equation, is reduced dimensionality of the problem by one order. Additionally, the mesh-free scheme eliminates the need for meshing, proving particularly beneficial for problems involving complex geometries. In this study, BNM is formulated using Element Free Galerkin (EFG) scheme to solve interior and exterior problems in acoustics. A 3-dimensional linear basis is used to construct moving least square shape functions. This eliminates the need to define additional local or parametric coordinate systems, making the method easily applicable to any arbitrary geometry. To illustrate the capabilities of the proposed method, four example problems are solved. An open pipe at resonance and a simple expansion muffler are analyzed to validate BNM’s performance in solving interior problems. Radiation from a pulsating sphere and radiation from a sphere with harmonic velocity excitation are analyzed as examples of exterior problems. Results from all four sample problems indicate that the BNM scheme proposed for solving acoustic problems is accurate and robust.

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解决室内外声学问题的边界节点法

边界节点法（BNM）是一种用于求解边界积分方程（BIE）的无网格方案。BNM 在两个层面上简化了问题。首先，由于 BNM 的目标是求解治理方程的积分形式，因此将问题的维度降低了一阶。此外，无网格方案消除了网格划分的需要，对于涉及复杂几何形状的问题尤其有利。在本研究中，BNM 采用无元素伽勒金（EFG）方案来解决声学中的内部和外部问题。三维线性基用于构建移动最小平方形状函数。这样就无需定义额外的局部或参数坐标系，从而使该方法可轻松适用于任何任意几何形状。为了说明所提方法的能力，我们解决了四个示例问题。分析了共振时的开放管道和简单的膨胀消声器，以验证 BNM 在解决内部问题方面的性能。作为外部问题的例子，分析了来自脉动球体的辐射和来自具有谐波速度激励的球体的辐射。所有四个示例问题的结果表明，为解决声学问题而提出的 BNM 方案是准确和稳健的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Computational Methods ENGINEERING, MULTIDISCIPLINARY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.30

自引率

17.60%

发文量

审稿时长

15 months

期刊介绍： The purpose of this journal is to provide a unique forum for the fast publication and rapid dissemination of original research results and innovative ideas on the state-of-the-art on computational methods. The methods should be innovative and of high scholarly, academic and practical value. The journal is devoted to all aspects of modern computational methods including mathematical formulations and theoretical investigations; interpolations and approximation techniques; error analysis techniques and algorithms; fast algorithms and real-time computation; multi-scale bridging algorithms; adaptive analysis techniques and algorithms; implementation, coding and parallelization issues; novel and practical applications. The articles can involve theory, algorithm, programming, coding, numerical simulation and/or novel application of computational techniques to problems in engineering, science, and other disciplines related to computations. Examples of fields covered by the journal are: Computational mechanics for solids and structures, Computational fluid dynamics, Computational heat transfer, Computational inverse problem, Computational mathematics, Computational meso/micro/nano mechanics, Computational biology, Computational penetration mechanics, Meshfree methods, Particle methods, Molecular and Quantum methods, Advanced Finite element methods, Advanced Finite difference methods, Advanced Finite volume methods, High-performance computing techniques.