A radial interpolation finite element method for 2D homogeneous and multifluid coupling acoustic problems

Abstract

In the acoustics Finite Element Method (FEM), the typical problems of the four-node isoparametric element are low accuracy and high sensitivity to the quality of mesh in the finite element mesh model. Therefore, a Radial Interpolation Finite Element Method (RIFEM), whose shape function is constructed by using the meshless radial interpolation technique and the partition-of-unity method, is proposed for the 2D homogeneous and multifluid coupling acoustic problems. In acoustic RIFEM, to maintain the integral accuracy of the sound pressure derivatives and apply the accurate boundary conditions easily, the acoustic system stiffness matrix and the vectors of the boundary integrals are constructed by using the bilinear shape function. On the contrary, to improve the interpolation accuracy of the approximated sound pressure function, the acoustic system mass matrix is constructed by the shape function of RIFEM using the four-node isoparametric element. Numerical examples on a 2D homogeneous acoustic tube, the 2D homogeneous acoustic cavity of a car and a 2D multifluid coupling tube verify that RIFEM achieves higher accuracy, when compared with the linear FEM and the smoothed FEM.