关键词: Helmholtz方程, 径向插值, 声学数值计算, 有限元法

Abstract: Aiming at the problems of low accuracy and sensitivity to the mesh’s quality of four-node isoparametric element in the acoustic finite element method (FEM), the radial interpolation finite element method (RIFEM), whose shape function is based on the meshless radial interpolation method, is proposed for two dimension acoustic problem. In acoustic RIFEM, the acoustic stiffness matrix and the vectors of the boundary integrals are constructed by the bilinear shape function, to maintain the integral accuracy of the sound pressure derivatives and the accurate boundary conditions applied on region boundary. The acoustic mass matrix is constructed by the shape function of the RIFEM by using the four-node isoparametric element, to improve the interpolation accuracy of the approximated sound pressure function. Numerical examples of a two-dimensional tube and a two-dimensional acoustic cavity of automobile are presented to show that RIFEM achieves higher accuracy, and is less sensitive to the wave number, the size of mesh, the level of mesh distortion as compared with FEM and SFEM. Hence the RIFEM can be well applied in solving two dimensional acoustic problems, and has a wide application foreground.

Key words: Acoustic numerical computation, Finite element method, Helmholtz equation, Radial interpolation method