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

作　　者：桂强 孙磊 游翔宇 柴应彬 李威[1,4,5] GUI Qiang;SUN Lei;YOU Xiang-yu;CHAI Ying-bin;LI Wei(School of Naval Architecture and Ocean Engineering,Huazhong University of Science and Technology,Wuhan 430074,China;School of Hydraulic and Environmental Engineering,Changsha University of Science&Technology,Changsha 410114,China;School of Naval Architecture,Ocean and Energy Power Engineering,Wuhan University of Technology,Wuhan 430063,China;Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics,Huazhong University of Science and Technology,Wuhan 430074,China;Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration(CISSE),Shanghai 200240,China)

机构地区：[1]华中科技大学船舶与海洋工程学院,武汉430074 [2]长沙理工大学水利与环境工程学院,长沙410114 [3]武汉理工大学船海与能源动力工程学院,武汉430063 [4]华中科技大学船舶与海洋水动力湖北省重点实验室,武汉430074 [5]高新船舶与深海开发装备协同创新中心,上海200240

出　　处：《计算力学学报》2024年第2期344-351,共8页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(52171336)资助项目.

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。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.

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 

分 类 号：O242.21[理学—计算数学] O302[理学—数学]