Simulation of the wave propagation in 1-D Zener's attenuative media

Computer simulation techniques, such as the Local Interaction Simulation Approach (LISA), can predict accurately and efficiently the propagation of acoustic and ultrasonic waves or pulses even in complex heterogeneous and anisotropic media. For a quantitative comparison with experimental results it is, however, necessary to properly include in the model the attenuation and dispersion properties of the propagation media. This is an interesting problem, even at the 1D level, due to the variety of models, which have been proposed to treat different classes of materials, and to the difficulty of solving, analytically or numerically, the corresponding equations, except in the simplest cases. In this paper Zener’s and other kinds of attenuative materials are examined in detail and an optimal discretization scheme is found, which yields stable and convergent simulations of the propagation mechanism. To illustrate the procedure several examples of propagation of monochromatic waves and pulses in different attenuative media are presented.