| Burton-Miller改进型边界方程的多频计算方法 |
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| 引用本文： | 刘宝,程广利,王德石.Burton-Miller改进型边界方程的多频计算方法[J].声学学报,2019,44(5):865-873. |
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| 作者姓名： | 刘宝 程广利 王德石 |
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| 作者单位： | 海军工程大学 武汉 430033 |
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| 基金项目： | 国家自然科学基金项目(11602300,11372350)资助 |
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| 摘 要： | 提出了一种采用Burton-Miller改进型边界积分方程进行多频计算的方法。将Burton-Miller方程中的高奇异积分转化为弱奇异积分形式,获得Burton-Miller改进型边界积分方程;将方程中格林函数进行Taylor级数展开,并把波数从方程中分离出来,从而使随波数变化的计算矩阵表示为波数的矩阵级数形式。数值分析表明,本方法不仅保证了解在全波数范围内的唯一性,并且计算频率点数较多时可以节约大量时间,提高计算效率。
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| 关 键 词： | Burton-Miller积分方程 弱奇异积分 Taylor级数 多频计算 |
| 收稿时间： | 2017-08-09 |
Multi-frequency calculation method of improved Burton-Miller boundary equation |
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| Affiliation: | Naval University of Engineering, Wuhan 430033 |
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| Abstract: | A method of multi-frequency calculation is proposed by using Burton-Miller improved boundary integral equation.The high singular integral in the Burton-Miller equation is transformed into a weakly singular integral form and Burton-Miller improved boundary integral equation is obtained.The Green function of the equation is expanded by Taylor series and the wavenumber is separated from the equation so that the calculation matrix in dependence of wave number is expressed as the matrix series associated with wavenumber.The numerical analysis shows that not only this method guarantees the uniqueness of solution in the range of full wavenumber,but also can save a lot of time and improve the calculation efficiency when there are many frequency points to be calculated. |
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