Numerical investigations of edge-based smoothed radial point interpolation method for transient wave propagations

Abstract

It is known that the solutions of the standard finite element method for transient wave propagations are suffering from the numerical dispersion effect and the numerical anisotropy, resulting in the dispersive numerical waves along different propagation angles. In this work, the edge-based smoothed radial point interpolation method is combined with the Bathe time integration method to study transient wave propagations. By means of the generalized gradient smoothing approach, the smoothed radial point interpolation method can lead to the proper smoothed stiffness of the discrete model, thus greatly reducing the numerical dispersion effect and the numerical anisotropy. Besides, due to the appropriate high-frequency dissipative property, the Bathe time integration method can effectively depress the spurious high-frequency responses in transient wave solutions. Moreover, the wave velocity errors of several numerical methods for transient wave propagations are theoretically and numerically analyzed, revealing the superiority of the smoothed radial point interpolation method in comparison with the linear and quadratic finite element methods. Several numerical tests show that the smoothed radial point interpolation method combined with the Bathe time integration method can present the more accurate simulations of transient wave propagations than the standard finite element method.