Simulation of the wave propagation in 1D Zener attenuative media

Computer simulation techniques, such as the Local Interaction Simulation Ap proach (LISA), can predict accurately and efficiently the propagation of ac oustic and ultrasonic waves or pulses even in complex heterogeneous and ani sotropic 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 pro blem, even at the 1D level, due to the variety of models, which have been p roposed to treat different classes of materials, and to the difficulty of s olving, analytically or numerically, the corresponding equations, except in the simplest cases. In this paper Zener's and other kinds of attenuative m aterials are examined in detail and an optimal discretization scheme is fou nd, which yields stable and convergent simulations of the propagation mecha nism. To illustrate the procedure several examples of propagation of monoch romatic waves and pulses in different attenuative media are presented.