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声学时域边界元法的时间卷积计算方法研究

朱寅弢 吴海军 孙瑞华 蒋伟康

朱寅弢, 吴海军, 孙瑞华, 蒋伟康. 声学时域边界元法的时间卷积计算方法研究[J]. 声学学报, 2023, 48(6): 1218-1226. doi: 10.12395/0371-0025.2022097
引用本文: 朱寅弢, 吴海军, 孙瑞华, 蒋伟康. 声学时域边界元法的时间卷积计算方法研究[J]. 声学学报, 2023, 48(6): 1218-1226. doi: 10.12395/0371-0025.2022097
ZHU Yintao, WU Haijun, SUN Ruihua, JIANG Weikang. A convolution quadrature method for acoustic time domain boundary element method[J]. ACTA ACUSTICA, 2023, 48(6): 1218-1226. doi: 10.12395/0371-0025.2022097
Citation: ZHU Yintao, WU Haijun, SUN Ruihua, JIANG Weikang. A convolution quadrature method for acoustic time domain boundary element method[J]. ACTA ACUSTICA, 2023, 48(6): 1218-1226. doi: 10.12395/0371-0025.2022097

声学时域边界元法的时间卷积计算方法研究

doi: 10.12395/0371-0025.2022097
详细信息
    通讯作者:

    吴海军, haijun.wu@sjtu.edu.cn

  • PACS: 43.20

A convolution quadrature method for acoustic time domain boundary element method

  • 摘要:

    核函数中保留Dirac函数的原型, 形成关于时间的卷积积分, 是声学时域边界元法中一种稳定、有效的时间数值积分计算方法(CQ-BEM)。然而, 传统CQ-BEM中卷积积分系数的获取有计算量大、耗时长, 且对不同单元需要重新计算的问题, 极大地降低了CQ-BEM法计算时域声场的效率。针对传统CQ-BEM积分系数计算效率低的问题, 本文利用多项式展开定理给出了待求函数泰勒系数的解析表达与数值计算方法, 建立了不同单元间待求系数的转换理论, 可以在一次循环迭代内完成不同单元的积分系数的计算, 大幅降低了计算量, 提高了CQ-BEM方法的声场计算效率。脉动球源数值算例结果表明, 在相同要求下, 本文方法计算时间较传统方法减少50%以上, 相对误差小5个数量级以上, 且计算时间随单元数的增长率仅为传统方法的2.34%。因此, 本文提出的系数计算方法能够有效提高CQ-BEM方法的时域声场计算效率, 拓展了CQ-BEM在大型机电设备时域声场模拟的计算规模。

     

  • 图 1  系数${\alpha _n}$计算相对误差$\varepsilon $与参数$L$$n$的关系

    图 2  球面网格模型

    图 3  脉动球源声场计算时间与网格单元数的关系

    图 4  观测点处声压仿真值与理论值对比 (a) 阶数n = 5; (b) 阶数n = 10; (c) 阶数n = 20; (d) 阶数n = 30

    图 5  二范数相对误差随阶数n变化曲线

    图 6  计算系数相对误差与计算时间的关系对比

    图 7  卷积系数${\alpha _n}$计算时间与网格数量的关系

    图 8  计算总时间与时间步关系

    表  1  截断项数 − 阶数(Ln)二次曲线拟合参数

    相对误差$a$$b$$c$
    ${10^{ - 2}}$−3.24408 × 10−32.75610 × 10−15.60391 × 100
    ${10^{ - 4}}$−3.39617 × 10−32.98290 × 10−18.42215 × 100
    ${10^{ - 6}}$−3.45414 × 10−33.11518 × 10−11.08118 × 101
    ${10^{ - 8}}$−3.47816 × 10−33.20749 × 10−11.29764 × 101
    ${10^{ - 10}}$−3.48680 × 10−33.27784 × 10−11.49946 × 101
    下载: 导出CSV

    表  2  卷积系数${\alpha _n}$关于重复计算次数x的线性拟合参数

    ${k_1}$${b_1}$
    传统方法1.73953×10−36.70258×10−3
    本文方法3.97174×10−51.95126×10−1
    下载: 导出CSV

    表  3  计算时间−迭代步数一次曲线拟合参数

    ${k_2}$${b_2}$
    传统方法5.20367×10−12.40009×103
    本文方法5.60708×10−14.86759×102
    下载: 导出CSV
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  • 被引次数: 0
出版历程
  • 收稿日期:  2022-10-09
  • 修回日期:  2022-12-24
  • 刊出日期:  2023-11-02

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