水槽动力特性数值模拟的新型局部无网格配点法  

A Novel Localized Meshless Collocation Method for Numerical Simulation of Flume Dynamic Characteristics

作　　者：曾维鸿 傅卓佳[1] 汤卓超 ZENG Weihong;FU Zhuojia;TANG Zhuoehao(College of Mechanics and Materials,Hohai University,Nanjing 211100,P.R.China)

机构地区：[1]河海大学力学与材料学院,南京211100

出　　处：《应用数学和力学》2022年第4期392-400,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12122205;11772119)。

摘　　要：局部边界节点法是一种基于非奇异半解析基函数和移动最小二乘原理的新型无网格配点技术,该方法把每个节点处的未知变量表示为该点对应的局部子域内节点处物理量的线性组合,该文基于局部边界节点法对数值波浪水槽进行了研究.首先,通过基准算例确定了Laplace算子非奇异半解析基函数的合理形状参数值.进一步,基于合理的参数选取,用较少的离散节点即可成功模拟波浪传播行为,将得到的数值结果与其他文献数值结果比较,可以发现局部边界节点法用更少的局部点即可得到较好的数值结果.最后,以保护近海岸建筑物为目标,模拟了水下防波堤对波浪传播的影响.结果表明,当波浪与梯形防波堤发生作用后,波峰变得比较陡峭,而波谷变得相对比较平坦,为近海岸防波堤的相关研究和设计提供了数值参考.The localized boundary knot method(LBKM) is a novel meshless collocation technology based on the nonsingular semi-analytical basis functions and the moving least squares theory, and expresses the unknown variable at each knot as a linear combination of physical quantities at nodes inside its corresponding local subdomain. The LBKM was used to study the numerical wave flume. Firstly, the appropriate shape parameters for the non-singular semi-analytical basis functions of the Laplace operator were derived by the benchmark example. Further, the numerical results obtained with fewer nodes and appropriate parameters were in good agreement with the referential results. Finally, the effects of the underwater breakwater on wave propagation were investigated to protect coastal buildings. The results show that, when the wave interacts with the trapezoidal breakwater, the wave crest will become steeper, and the wave trough will become relatively flatter, which provides a numerical reference for the research and design of the coastal breakwater.

关 键 词：局部边界节点法 无网格方法 非奇异半解析基函数 波浪 防波堤 

分 类 号：O353.4[理学—流体力学]