UNO Modifications of the Godunov Method for Calculating the Dynamics of an Elastic-Plastic Body

Abstract

Two UNO modifications of the Godunov method for calculating waves in an elastic-plastic body are presented, both being of the second order of accuracy in space and time. The waves are governed by the differential equations in the hydrostatic pressure and the components of the velocity vector and the deviator of the stress tensor. The solid plasticity is taken into account by the von Mises condition. In the first UNO modification, the unknown functions of the governing equations are determined using the invariants reconstructed by their grid cell values. In the second modification, the invariants are not applied. Instead, the unknown functions themselves are reconstructed by their cell values. The first modification better resolves the interaction of discontinuities, whereas the second one is algorithmically simpler. The latter can be useful in simulating multidimensional problems. These features of the presented modifications are illustrated by one- and two-dimensional problems.