Numerical Study of the Compartment Cavity Problem Using a Novel Cell-Based Smoothed Radial Point Interpolation Method

Nowadays, the finite element method (FEM) is used to predict the performance of vehicle compartment cavity, i.e. the acoustic modal, the acoustic frequency response, etc. The accuracy of conventional FEM for acoustic problem strongly depends on the size of the mesh, element quality, etc. As element size gets greater and distortion gets severer, the deviation of high wave number problem also gets larger. In order to improve the accuracy of acoustic problem, this paper introduces a novel cell-based smoothed radial point interpolation method (CS-RPIM) to solve the vehicle compartment cavity model. In present method, the cavity is discretized using tetrahedron background cells, the each cell is further divided into four smoothing cells and then the cell-based gradient smoothing operation is implemented through the smoothing cells. The system equations are derived using the smoothed Galerkin weak form, and the essential boundary conditions are imposed directly as in the finite element method (FEM).The cell-based gradient smoothing operation provides proper softening effect, makes the CS-RPIM model much softer than the “overly-stiff” FEM model and hence significantly reduces the “pollution effect”. The present method is implemented to predict the vehicle compartment acoustic modal analysis and the acoustic frequency response analysis. Both the results show that the present method can provide more accurate results compared with the standard FEM using the same mesh. It indicates that the present CS-RPIM can be widely applied to solving many engineering NVH problems with more accurate solutions.