UNO and TVD schemes for calculation of waves in an elastic-plastic body

Abstract

TVD and UNO schemes for efficiently calculating one-dimensional waves in an elastic-plastic body are presented. Both schemes are of the second order of accuracy, with an exception for the TVD scheme in the local extrema of the solution where its accuracy is reduced to the first order. The waves in the body are governed by differential equations in the hydrostatic pressure and the components of the velocity and the deviator of the stress tensor. The plasticity of the body is taken into account using the Mises condition. The classical Godunov method is used for estimating the effectiveness of the presented schemes. It is shown that on the same computational grids, the accuracy of the numerical results by the presented schemes significantly exceeds the accuracy of the results by the Godunov method. At the same time, the UNO scheme is more preferable, since the TVD scheme cuts the solution extrema because it strictly satisfies the TVD condition.