Numerical simulation and visualization of elastic waves using mass-spring lattice model

Abstract

A computer program package has been developed for simulation and visualization of two-dimensional elastic wave propagation and scattering using the mass-spring lattice model (MSLM) and, for comparison, a finite difference model. To assess the reliability of the numerical schemes, their convergence and accuracy have been analyzed using the Taylor series expansion and the von Neumann analysis methods. As a result, the grid spacing-time increment combinations previously adopted in the literature have proved to be non-optimal. The optimal combinations have been found and shown to yield the most accurate results with the least computation time, particularly in the high frequency regime. Using these algorithms, a program package has been developed in Visual C++(R) (Microsoft, Redmond, WA) with graphic user interfaces for convenient exploration of visualized results. Numerical results have been obtained for some fundamental problems in ultrasonic testing such as plane waves incident on cracks. All numerical results have shown excellent qualitative agreements with the analytical results of the wave physics, as the reflected, diffracted, head, and Rayleigh waves have been observed. Also, for numerical results with anisotropic media, the cusps on the shear wavefronts have been observed. Finally slight modification of the modeling method for free surfaces has led to more accurate prediction of Rayleigh waves.