Finite-Difference Time-Domain Numerical Analysis of Elastic Wave Fields Using both Elastic and Velocity Potential Variables

Abstract

The use of both elastic variables and velocity potentials is proposed for the analysis of elastic wave fields in isotropic solids by finite-difference time-domain (FDTD) methods. The term 'elastic variables' refers to stresses and particle velocities. Velocity potentials can be directly derived using the same leap-frog finite-difference scheme as in the FDTD method. In some situations, for example, where an absorbing boundary is present, it is more straightforward to calculate using velocity potentials. This approach also provides an easy way to handle of complex elastic wave phenomena. On the other hand, many other types of boundary conditions are often expressed in terms of elastic variables. In these situations, it is more convenient to use elastic variables for calculation. Some examples are introduced here to illustrate the efficiency of the proposed technique. First, the method was used for the case of an absorbing boundary. In the model, almost all analysis was carried out using values of stress and particle velocity, but velocity potentials were applied near the absorbing boundary on the truncated interface. Second, an interface between elastic variables and velocity potentials, namely a stress-velocity/potentials interface, was constructed around a scattering object. External to the interface, stresses and particle velocities were used for calculation, and potential variables were applied inside the interface. In a third example, calculations were made over almost the entire analytical region using potential values, but in the neighborhood of the free boundary, elastic variables were used. All the examples above were analyzed numerically using the FDTD method, and the results confirmed the usefulness of the method.

Verification of the influence of liver microstructure on the evaluation of shear wave velocity

“…Equations ( 1) and ( 2) describe Hooke's law and Newton's second law of motion, respectively. [37][38][39][40][41] In these equations, u x and u z represent the particle velocity in the lateral and depth directions, respectively, while T x and T z are normal stresses, and T xz represents shear stress. In addition, ρ, λ, and μ represents density, Lame's first coefficient, and Lame's second coefficient (the elastic shear coefficient), respectively, which indicate the elastic information of the tissues.…”

“…19,23,24,32) The present study attempts to verify the influence of liver microstructure (fat droplets and fibrous tissue) on SWV evaluation using shear wave propagation simulation. 36) Propagated shear waves in fatty liver, fibrotic liver, and NASH liver containing both fat droplets and fibrous tissue were simulated with 10 μm analytical elements using the elastic finite-difference time-domain (FDTD) [37][38][39][40][41] method, which allows calculation of the time change of elastic wave propagation. By comparing the shear waveform and SWV evaluation for each liver on the ultrasound microscope level (microscale) and the diagnostic equipment level (macroscale), we investigated the relationship between the liver microstructure and the shear wave propagation.…”

Characterization of contact condition in a flange connection by longitudinal waves

“…The IF is therefore expected to be a suitable parameter for contact condition estimation. To clarify the behavior of the IF change in the transmission and reflection waves with the pressure, a onedimensional numerical calculation with a finite difference time domain (FDTD) method (Sato, 2006) was performed. Figure 5 shows the one-dimensional numerical calculation model used in this study.…”

Interface wave propagation and edge conversion at a low stiffness interphase layer between two solids: A numerical study

“…To interpret their behavior to predict the Rayleigh wave conversion to/from the interface waves is essential. We perform analysis and visualization of the wave interaction and conversion by a finite-difference time-domain (FDTD) method adapted from [19]. A computation algorithm was coded and implemented in house.…”

“…These two components were calculated alternatively according to the leap-frog scheme for the individual governing equations following [19]. where T xx , T yy and T xy are stress components, and _ u x and _ u y are particle velocities along the x and y direction, respectively.…”