Abstract
SUMMARYAn 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. Copyright © 2012 John Wiley & Sons, Ltd.
Highlights
High-fidelity analysis of wave propagation problems in damping-free homogeneous solids is obtained by a combination of three ingredients: the discrete equations of motion with regular uniform and equal mesh lengths, an explicit integrator with no numerical damping and minimum phase error, and the integration step size that satisfies the Courant number (C r D ct =x) to be unity, where .c, t, x/ are the speed of the sound of the material, the time step and the characteristic element length, respectively
This ideal combination is difficult to realize, an acceptable compromise can often be achieved for discontinuous wave propagation analysis of homogeneous solids
It is generally recognized that wave propagation analysis tools primarily developed for homogeneous solids become inadequate for heterogeneous materials, so much so that we are back to rely heavily on experiments, instead of complementing with simulation to a great extent, for material characterization of most of new synthesized materials for dynamic applications
Summary
High-fidelity analysis of wave propagation problems in damping-free homogeneous solids is obtained by a combination of three ingredients: the discrete equations of motion with regular uniform and equal mesh lengths, an explicit integrator with no numerical damping and minimum phase error, and the integration step size that satisfies the Courant number (C r D ct =x) to be unity, where .c, t , x/ are the speed of the sound of the material, the time step and the characteristic element length (or mesh size), respectively. (3) Employ variable step sizes for each of heterogeneous zones to minimize spurious oscillations inherent for all the existing integration schemes when the step size is different from the ideal one, namely C r D ct =x D 1. It will be shown that the proposed method significantly alleviates spurious oscillations when the integration step sizes are different from the critical stepsize, namely ct =x < 1.
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