A Cell-Based Smoothed Radial Point Interpolation—Perfectly Matched Layer Method For Two-Dimensional Acoustic Radiation Problems

Abstract

We present a cell-based smoothed radial point interpolation method (CS-RPIM) model for two-dimensional acoustic radiating problem by incorporating the perfectly matched layer method (PML). In this work, the computational region, truncated by PML, is discretized into triangular background cells. Each cell is further divided into several smoothing cells, and then the cell-based gradient smoothing operation is implemented throughout the smoothing cells. The pressure field function is approximated using the RPIM shape functions. The supporting node selection for shape function construction uses the T2L-scheme associated with edges of the background cells. The cell-based gradient smoothing operation provides proper softening effect, and makes the acoustic stiffness of the CS-RPIM model much softer than that of the FEM (finite element method)/PML model, which in turn significantly reduces the numerical dispersion error. Numerical results show that, compared with FEM–PML, the CS-RPIM achieves better absorbing effect in the PML, and higher accuracy in the computational region. This enables us to conclude that the CS-RPIM model with the PML can be well applied in solving acoustic radiation problems.