Modified Godunov's Scheme for Modeling the Spatial Impact Interaction of Bodies with Soil Media

The previously developed two-dimensional numerical technique for modeling high-speed shock-wave interaction of solid deformable bodies with soil media at large displacements and deformations in Euler variables is developed for the general three-dimensional case. Ground media are considered as elastoplastic media with irreversible volumetric and shear deformations. The numerical technique is based on the use of a modified Godunov scheme of increased accuracy and Euler-Lagrangian multigrid algorithms. The solution of the elastic Riemann problem for the spatial stress-strain state is used, which depends on time and provides the second order of approximation in time and space in the region of smooth solutions. The results of modeling the processes of normal and inclined high-speed impact interaction of bodies with soil media with and without friction forces are presented. The results are compared with known experimental.