Application of the Godunov Scheme to Solve Three-Dimensional Problems of High-Speed Interactions of Elastoplastic Bodies

A 3D technique for modeling the high-speed shock-wave interaction of solid deformable bodies with large displacements and deformations in Euler variables is developed. 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 problem of discontinuity decay for a 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. Three types of computational grids are used for each interacting body with an explicit Lagrangian selection of movable free and contact surfaces. The first type is a Lagrangian surface grid in the form of a continuous set of triangles, which is used both to set the initial geometry of the solid body and to accompany it during the calculation process, and two types of three-dimensional volumetric grids: a basic Cartesian fixed grid for each body, and auxiliary movable local Euler–Lagrangian grids associated with each triangle of the surface grid. The results of testing the methodology and modeling the processes of the high-speed impact interaction of bodies and deep penetration of deformable impactors into elastic-plastic barriers are presented.