On space and time step sizes in rectangular finite element meshes for ultrasonic pulse propagation

Abstract

he focus of the work is to analyse and improve the accuracy of space and time discretized rectangular finite element models for transient acoustic wave propagation. The propagation of the typical ultrasonic pulse excited on the boundary of the environment is under investigation. The dispersion relations of finite element models have been significantly improved by selecting appropriate form of the mass matrix. As a consequence, only 5 elements per wavelength suffice to represent satisfactory the wave propagation law. As contraindication for using such an approach is a non-diagonal form of the mass matrix requiring to use iterative methods for solving the linear algebraic equation system at each time step. However in 2D and 3D cases the increase of the element size results in considerable savings in memory and computational time even if iteration at each time step is necessary. With increased element size the accuracy requirement instead of stability is dominating for the selection of the time step. The explicit time integration schemes in the case of non-diagonal mass matrix have no computational advantage, and implicit ones can be discussed. The performance of several numerical integration schemes has been evaluated in this study. From the point of view of combined performance and accuracy criterion, the 3-rd order generalized Newmark's scheme has been selected.