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水槽动力特性数值模拟的新型局部无网格配点法

曾维鸿 傅卓佳 汤卓超

曾维鸿,傅卓佳,汤卓超. 水槽动力特性数值模拟的新型局部无网格配点法 [J]. 应用数学和力学,2022,43(4):392-400 doi: 10.21656/1000-0887.420246
引用本文: 曾维鸿,傅卓佳,汤卓超. 水槽动力特性数值模拟的新型局部无网格配点法 [J]. 应用数学和力学,2022,43(4):392-400 doi: 10.21656/1000-0887.420246
ZENG Weihong, FU Zhuojia, TANG Zhuochao. A Novel Localized Meshless Collocation Method for Numerical Simulation of Flume Dynamic Characteristics[J]. Applied Mathematics and Mechanics, 2022, 43(4): 392-400. doi: 10.21656/1000-0887.420246
Citation: ZENG Weihong, FU Zhuojia, TANG Zhuochao. A Novel Localized Meshless Collocation Method for Numerical Simulation of Flume Dynamic Characteristics[J]. Applied Mathematics and Mechanics, 2022, 43(4): 392-400. doi: 10.21656/1000-0887.420246

水槽动力特性数值模拟的新型局部无网格配点法

doi: 10.21656/1000-0887.420246
基金项目: 国家自然科学基金(12122205;11772119)
详细信息
    作者简介:

    曾维鸿(1996—),男,硕士生(E-mail:1021211875@qq.com

    傅卓佳(1985—),男,教授,博士,博士生导师(通讯作者. E-mail:paul212063@hhu.edu.cn

    汤卓超(1994—),男,博士生(E-mail:MrTangZC@163.com

  • 中图分类号: O353.4

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

  • 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。

  • 图  1  数值波浪水槽的示意图

    Figure  1.  The schematic diagram of the numerical wave flume

    图  2  $x = 4$处自由液面高程演化图:(a)不同总节点数;(b)不同时间间隔;(c)不同邻近点数

    Figure  2.  Evolution of free-surface elevation at $x = 4 :$ (a) different total numbers of nodes; (b) different time increments; (c) different numbers of nearest nodes

    图  3  自由表面在4个不同时刻的轮廓

    Figure  3.  Profiles of free surface along the flume at 4 specific moments

    图  4  梯形防波堤数值波浪水槽的示意图

    Figure  4.  The schematic diagram of the numerical wave flume with a trapezoidal submerged obstacle

    图  5  梯形防波堤数值波浪水槽的布点图

    Figure  5.  Distributions of nodes of the numerical wave flume with a trapezoidal submerged obstacle

    图  6  最后两个周期的高程演化

    Figure  6.  Elevation evolution of the last 2 periods

    图  7  自由液面从$x = 6$$x = 17$在特定时刻的表面轮廓

    Figure  7.  Free surface profiles from $x = 6$ to $x = 17$ at specific moments

    表  1  不同形状参数下二阶Stokes波的均方根误差

    Table  1.   The RMSEs for 2nd-order Stokes waves with different shape parameters

    $c$0.010.10.511.522.533.2
    εRMSE1\$5.23 \times {10^{ - 3}}$$6.13 \times {10^{ - 4}}$$5.81 \times {10^{ - 4}}$$6.16 \times {10^{ - 4}}$$6.50 \times {10^{ - 4}}$$6.84 \times {10^{ - 4}}$$7.19 \times {10^{ - 4}}$\
      注:“\”表示无法计算,后同。
      Note: “\” means unable to calculate, the same below.
    下载: 导出CSV

    表  2  不同总点数下LBKM与GFDM的均方根误差

    Table  2.   The RMSE1s of LBKM and GFDM under different total numbers of nodes

    $N$88933791315920449
    LBKM$7.28 \times {10^{ - 4}}$$6.18 \times {10^{ - 4}}$$5.81 \times {10^{ - 4}}$$5.78 \times {10^{ - 4}}$
    GFDM$5.98 \times {10^{ - 3}}$$1.28 \times {10^{ - 3}}$$4.71 \times {10^{ - 4}}$$4.63 \times {10^{ - 4}}$
    下载: 导出CSV

    表  3  不同邻近点数下LBKM与GFDM的均方根误差

    Table  3.   The RMSE1s of LBKM and GFDM under different numbers of nearest nodes

    $m$610141618202530
    LBKM$5.04 \times {10^{ - 3}}$$6.13 \times {10^{ - 4}}$$5.91 \times {10^{ - 4}}$$5.85 \times {10^{ - 4}}$$5.82 \times {10^{ - 4}}$$5.81 \times {10^{ - 4}}$$6.53 \times {10^{ - 4}}$$2.56 \times {10^{ - 3}}$
    GFDM\\$4.78 \times {10^{ - 4}}$$4.77 \times {10^{ - 4}}$$4.75 \times {10^{ - 4}}$$4.71 \times {10^{ - 4}}$$2.34 \times {10^{ - 3}}$$3.58 \times {10^{ - 3}}$
    下载: 导出CSV

    表  4  不同总点数下$\phi $${{\partial \phi } / {\partial x}}$${{{\partial ^2}\phi } / {\partial {x^2}}}$的均方根误差

    Table  4.   The RMSE2s of $\phi $, ${{\partial \phi } / {\partial x}}$ and ${{{\partial ^2}\phi } / {\partial {x^2}}}$ under different total numbers of nodes

    $N$88933791315920449
    $\phi $$4.63 \times {10^{ - 3}}$$3.85 \times {10^{ - 3}}$$2.42 \times {10^{ - 3}}$$2.35 \times {10^{ - 3}}$
    ${{\partial \phi }/{\partial x}}$$1.29 \times {10^{ - 2}}$$6.65 \times {10^{ - 3}}$$6.52 \times {10^{ - 3}}$$5.26 \times {10^{ - 3}}$
    ${{{\partial ^2}\phi } / {\partial {x^2}}}$$3.96 \times {10^{ - 2}}$$2.86 \times {10^{ - 2}}$$2.58 \times {10^{ - 2}}$$1.26 \times {10^{ - 2}}$
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-08-20
  • 修回日期:  2021-10-05
  • 网络出版日期:  2022-03-21
  • 刊出日期:  2022-04-01

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