Calculation of Waves in an Elastic-Plastic Body Based on ENO Modifications of the Godunov Method

The efficiency of two ENO modifications of the Godunov method for calculation axisymmetric problems of the dynamics of elastic-plastic bodies, namely a UNO scheme of the second-order of accuracy and a TVD scheme of the second order of accuracy outside the solution extremes where it decreases to the first order, has been numerically studied. The efficiency of the modifications is estimated by comparing the results of calculation of a number of problems on the propagation of spherical and cylindrical waves in a body with the results of reference solutions and the Godunov method. The exact and numerical solutions are used as reference solutions, the latter are obtained on fine grids. It is shown that for all the problems considered, the solutions by the TVD and UNO schemes are much closer to the reference ones than those by the Godunov method. The TVD and UNO schemes are characteristic of significantly less smearing of sharp wave fronts and a more accurate resolution of extrema. At the same time, the wave profiles and the extrema are reproduced by the UNO scheme somewhat better than by the TVD scheme.