A method for computation of discontinuous wave propagation in heterogeneous solids: Basic algorithm description and application to one-dimensional problems

摘要

An explicit integration algorithm for computations of discontinuous wave propagation in heterogeneous solids is presented, which is aimed at minimizing spurious oscillations when the wave fronts pass through several zones of different wave speeds. The essence of the present method is a combination of two wave capturing characteristics: a new integration formula that is obtained by pushforward-pullback operations in time designed to filter post-shock oscillations, and the central difference method that intrinsically filters front-shock oscillations. It is shown that a judicious combination of these two characteristics substantially reduces both spurious front-shock and post-shock oscillations. The performance of the new method is demonstrated as applied to wave propagation through a uniform bar with varying courant numbers, then to heterogeneous bars.