Computation of waves in elastic-plastic body

A.A. Aganin*, N.A. Khismatullina**

Institute of Mechanics and Engineering,

Kazan Science Center, Russian Academy of Sciences, Kazan, 420111 Russia

E-mail: *ganin@kfti.knc.ru, **nailya_hism@mail.ru

Received March 7, 2018

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Abstract

To study wave propagation in continuous media, the classical Godunov method, which is stable and monotonic, is widely used. However, due to the first order of accuracy, it can lead to strong smearing of jumps, contact discontinuities, and other features of the solution in regions with large gradients. The possibility of increasing the computational efficiency of the elastic-plastic waves in a body in comparison with the Godunov method by applying its TVD- and UNO-modifications has been investigated in this paper. The UNO-modification is strictly second-order accurate, whereas the TVD-modification loses that accuracy at the solution extrema due to exactly satisfying the condition of total variation diminishing, while the UNO-modification meets it approximately. The plastic state of the body has been described by the Mises condition. Estimation of the efficiency of the considered modifications has been carried out by comparing the results of their application to a number of problems with the results obtained by the Godunov method. Problems of the propagation of 1D plane elastic-plastic waves have been considered. Those waves result in a body from the action of a pressure pulse on its surface or the given impulsive displacement of the surface. It has been shown that on the same computational grids the results of the considered modifications are much better than those obtained by the Godunov method. In particular, the width of smearing the jump-like fronts of both the elastic and plastic waves is significantly less. At that, the UNO-modification is more preferable because the TVD-modification tends to "cut'' the solution extrema.

Keywords: TVD scheme, UNO scheme, Godunov scheme, efficiency of difference schemes, elastic-plastic body

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For citation: Aganin A.A., Khismatullina N.A. Computation of waves in elastic-plastic body. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, vol. 160, no. 3, pp. 435-447. (In Russian)

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