Finite-Difference Time Domain Method. Calculating Echo Signals in Homogeneous Isotropic Materials

The method of finite differences in time domain (FDTD) can be used to calculate echo signals in numerical ultrasonic-inspection experiments. As the FDTD method is based on the explicit numerical solution of the wave equation for elastic medium, it can be used to take account of the emergence of a run round wave on a bulk reflector, the effects of a longitudinal wave transforming into a lateral one in the scattering of ultrasound on a crack, and rescattering of pulses between reflectors and test object boundaries. Numerical solution of the vector wave equation by the FDTD method, in contrast to the modelling methods based on the theory of ray tubes, enables a more accurate modeling of ultrasonic inspection results. In this article, three options are considered for suppressing pulse reflections from computational grid boundaries. Calculating the direct problem of the propagation of elastic vibrations through a solid body by the FDTD method may prove useful when solving the inverse coefficient problem of nondestructive ultrasonic inspection.