Numerical modeling elasto-plastic flows by using a Godunov method with moving Eulerian grids

The paper addresses a numerical method for calculating elasto-plastic flows on arbitrary moving Eulerian grids. The Prandtl-Reus model is implemented in the system of governing equations to describe elasto-plastic properties of solids in dynamical processes. The spatial discretization of the equations is carried out with the Godunov method applied to a moving Eulerian grid. Piecewise-linear cell data reconstruction is implemented using a MUSCL-type interpolation procedure with generalization on unstructured grids to improve accuracy of the scheme. The main idea of method is composed of splitting system of governing equations into hydrodynamical and elastoplastic components. The hydrodynamical part of equations is updated in time with an absolutely stable explicit-implicit time marching scheme. The solution to the constitutive equations is obtained with the second order Runge–Kutta scheme. The theoretical analysis is carried out and analytical solutions are presented that describe the shock-wave structure and the structure of a rarefaction wave in elasto-plastic materials under uniaxial deformation assumption. The method is verified by calculating the problems with presented analytical solutions, and also comparing on some test problems calculated by other authors with different numerical methods.