| 桂强,孙磊,游翔宇,柴应彬,李威.二维水下声辐射问题的改进径向基点插值法研究[J].计算力学学报,2024,41(2):344~351 |
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| 二维水下声辐射问题的改进径向基点插值法研究 |
| A modified radial point interpolation method for the analysis of underwater acoustic radiation problems |
| 投稿时间：2022-06-01 修订日期：2022-09-02 |
| DOI：10.7511/jslx20220601001 |
| 中文关键词: 径向基点插值法 水下声辐射 DtN映射 无界域 无网格技术 |
| 英文关键词:radial point interpolation method underwater acoustic radiation problems DtN mapping infinite domain meshless technique |
| 基金项目:国家自然科学基金（52171336）资助项目. |
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| 摘要点击次数: 271 |
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| 中文摘要: |
| 径向基点插值法是一种典型的无网格数值计算方法,在分析声学问题时,相比于传统有限元法能更好地抑制频散误差,且在相同的节点分布下通常可以得到更精确的数值解。本文提出一种改进的节点选取方案用于构造插值形函数,即改进径向基点插值法。该方案采取一个简单而直接的格式,可确保在进行数值积分时同一背景积分单元中的被积函数是连续可微的,从而减小数值积分误差,得到比原始径向基点插值法更精确的数值解。同时,为了处理外声场问题,本文采用DtN映射技术将无限域截断为有界计算域,满足索默菲尔德辐射条件。数值试验表明,相比于传统有限元法和原始径向基点插值法,本文改进方法具有更高的计算精度和计算效率,在研究水下声辐射问题时具有良好的应用前景。 |
| 英文摘要: |
| The radial point interpolation method (RPIM),a typical meshless technique,outperforms the classic finite element method (FEM) in suppressing the numerical dispersion errors and generating more accurate solutions using the same node distributions in acoustic analyses.In this work a modified node selection scheme for the construction of shape functions is developed and the proposed method is termed the modified RPIM (mRPIM).This scheme employs a simple and effective form which makes the integrand inside an identical background cell compatible.Thus,the integration error is significantly reduced and the solution accuracy is improved.Meanwhile,the Dirichlet-to-Neumann (DtN) mapping technique is utilized to make the infinite domain a bounded computational domain and the Sommerfeld radiation condition can be satisfied.Numerical experiments show that the proposed mRPIM can yield more accurate solutions and be more efficient than the standard FEM and the standard RPIM,and is promising in solving underwater acoustic radiation problems. |
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