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| 二维多流体域声传播计算的弱形式无网格方法 |
| A weak-form meshfree method for two-dimensional acoustic wave propagation in multi-fluids |
| 投稿时间：2024-05-09 修订日期：2024-06-11 |
| DOI： |
| 中文关键词: 多流体域声传播, 有限元法, 弱形式无网格法, 罚函数法, 计算声学 |
| 英文关键词:Acoustic propagation in multi-fluids, Finite element method, Weak-form meshfree method, Penalty function method, Computational acoustics |
| 基金项目:国家自然科学基金项目（面上项目）；湖南省教育厅科学研究项目 |
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| 摘要点击次数: 54 |
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| 中文摘要: |
| 多流体域声传播研究在船海工程中具有重要的应用价值，如气液共存的管道声传播分析、海底掩埋物探测等。经典有限元法求解此类问题时存在两个难点：一是中高波数下解中存在严重的数值色散误差；二是耦合界面附近必须使用精细网格。这些难点导致有限元法的计算量较庞大，需人工干预以生成高质量网格。与有限元法相比，弱形式无网格法无需传统意义上的网格划分，其解中的色散误差效应更弱，保证了良好的计算精度及效率，但无网格形函数具有不连续性质，导致质点振速连续条件无法在界面上自然满足。因此，本文提出了多流体域声传播计算的无网格伽辽金弱形式，运用罚函数法重构了界面上的质点振速连续条件。数值分析表明，无网格解与参考解相符，且计算精度及效率优于有限元解。 |
| 英文摘要: |
| Research on acoustic propagation in multi-fluids has important application values in naval architecture and ocean engineering, such as the acoustic propagation in pipelines filled with water and air, and the detection of buried objects. There are two difficulties in solving such problems with the use of the classical finite element method: one is the serious numerical dispersion error in the finite element solutions under medium and high wave numbers; the other is the need to use refined mesh grids to discretize the fluids near the coupling interface. These difficulties lead to a large computational cost for the finite element method, and the manual intervention to generate refined meshgrids. Compared with the finite element method, the weak-form meshfree method does not require traditional meshgrids, and the dispersion error effect in its solution is much weaker, ensuring good computational accuracy and efficiency. However, the meshfree shape functions are usually discontinuous in the problem domain, resulting in the inability of the continuity condition of the acoustic particle velocity to be naturally satisfied on the interface. Therefore, this paper uses the penalty function method to reconstruct the continuity condition of the acoustic particle velocity on the interface, and proposes a Galerkin weak form suitable for meshfree methods for acoustic propagation in multi-fluids. Numerical analysis shows that the meshfree solutions is consistent with the reference solutions, and the computational accuracy and efficiency of the meshfree method can be better than the finite element solutions. |
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