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.