二维多流体域耦合声场的光滑有限元解法

针对声学有限元分析中四节点等参单元计算精度低,对网格质量敏感的问题,将光滑有限元法引入到多流体域耦合声场的数值分析中,提出了二维多流体域耦合声场的光滑有限元解法。该方法在Helmholtz控制方程与多流体域耦合界面的声压/质点法向速度连续条件的基础上,得到二维多流体耦合声场的离散控制方程,并采用光滑有限元的分区光滑技术将声学梯度矩阵形函数导数的域内积分转换形函数的域边界积分,避免了雅克比矩阵的计算。以管道二维多流体域耦合内声场为数值分析算例,研究结果表明,与标准有限元相比,对单元尺寸较大或扭曲严重的四边形网格模型,光滑有限元的计算精度更高。因此光滑有限元能很好地应用于大尺寸单元或扭曲严重的网格模型下二维多流体域耦合声场的预测,具有良好的工程应用前景。

A smoothed finite element method for two-dimensional coupling acoustic fields in multi-fluid domain

Aiming at the typical problem of low accuracy and high sensitivity to the mesh's quality in the acoustic finite element method (FEM) analysis by using four-node isoparametric elements,a smoothed finite element method (SFEM) is proposed for the numerical analysis of the coupling acoustic fields in multi-fluid domain.In this method,the finite element control equation,based on Helmholtz equation and the continuous condition of acoustic pressure/particle normal velocity,is derived.The domain integrals of shape function gradients in acoustic pressure gradient matrix are recast into boundary integrals of shape functions by using cell-wise smoothing operation of SFEM and the computation of Jacobi matrix is avoided.The numerical example of a two-dimensional coupling acoustic field in multi-fluid domain of tube shows that SFEM achieves higher accuracy as compared with FEM when the sizes of elements are large or the quadrilateral meshes are seriously distorted.Hence,the SFEM can be well applied in analyzing two dimensional coupling acoustic fields in multi-fluid domain with large size elements or very irregular meshes,and has a wide application foreground.