Gradient viscoelastic virtual boundary for numerical simulation of wave propagation

A type of artificial boundary layer for the numerical simulation of wave propagation, which is named the gradient viscoelastic (GV) boundary layer, is proposed in this study. The setting of the GV boundary layer was established according to the propagation behavior of the longitudinal wave in the elastic GV rod, the analytical solution of the longitudinal wave propagation in the GV rod was obtained via the Wentzel–Kramers–Brillouin (WKB) method, and the zero-reflection and attenuation condition was determined. The settings of the GV boundary layer in the 1D and 2D time-domain simulations were applied to numerical examples and then compared. Numerical results showed that setting the GV boundary layer in the structure could remarkably reduce the error caused by truncation, and the combined GV boundary and low-reflection (LR) boundary presented the best combination. These results provide a simple method for artificial boundary layer setting to solve numerical wave simulations in the time domain.