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首页> 外文期刊>Journal of Computational Physics >Acoustic scattering by multiple elliptical cylinders using collocation multipole method
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Acoustic scattering by multiple elliptical cylinders using collocation multipole method

机译：搭配多极子法在多个椭圆圆柱体上的声散射

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This paper presents the collocation multipole method for the acoustic scattering induced by multiple elliptical cylinders subjected to an incident plane sound wave. To satisfy the Helmholtz equation in the elliptical coordinate system, the scattered acoustic field is formulated in terms of angular and radial Mathieu functions which also satisfy the radiation condition at infinity. The sound-soft or sound-hard boundary condition is satisfied by uniformly collocating points on the boundaries. For the sound-hard or Neumann conditions, the normal derivative of the acoustic pressure is determined by using the appropriate directional derivative without requiring the addition theorem of Mathieu functions. By truncating the multipole expansion, a finite linear algebraic system is derived and the scattered field can then be determined according to the given incident acoustic wave. Once the total field is calculated as the sum of the incident field and the scattered field, the near field acoustic pressure along the scatterers and the far field scattering pattern can be determined. For the acoustic scattering of one elliptical cylinder, the proposed results match well with the analytical solutions. The proposed scattered fields induced by two and three elliptical-cylindrical scatterers are critically compared with those provided by the boundary element method to validate the present method. Finally, the effects of the convexity of an elliptical scatterer, the separation between scatterers and the incident wave number and angle on the acoustic scattering are investigated.
机译：本文提出了一种配位多极方法，用于处理多个椭圆圆柱体在入射平面声波的作用下引起的声散射。为了满足椭圆坐标系中的亥姆霍兹方程，根据角和径向Mathieu函数来表示散射声场，该函数也满足无穷远处的辐射条件。通过在边界上均匀配置点，可以满足软边界或硬边界的条件。对于声强或诺伊曼条件，声压的正态导数是通过使用适当的方向导数确定的，而无需Mathieu函数的加法定理。通过截断多极展开，可以导出有限线性代数系统，然后可以根据给定的入射声波确定散射场。一旦将总场计算为入射场和散射场的总和，就可以确定沿散射体的近场声压和远场散射模式。对于一个椭圆圆柱体的声散射，所提出的结果与解析解吻合得很好。将由两个和三个椭圆圆柱散射体引起的拟议散射场与边界元方法提供的散射场进行了严格比较，以验证本方法。最后，研究了椭圆形散射体的凸度，散射体之间的间隔以及入射波数和入射角对声散射的影响。

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