Numerical modeling of spatial problems of hydrodynamics taking into account elastic processes

In the present work, the support operator method for spatial problems of elasticity theory is used to construct a finite-difference approximation of elastic forces on staggered Lagrangian meshes. For displacement vectors on irregular meshes, as applied to difference schemes, for problems of elasticity theory, the corresponding discrete operations have been developed. Taking into account the energy balance of the medium, the presented families of integrally consistent approximations of vector analysis operations are sufficient for numerical modeling of these processes. The resulting forces acting on the nodal domains of the medium are obtained explicitly in two-dimensional and three-dimensional geometry. Calculations are given for the propagation of sound waves in an aluminum three-dimensional orthogonal plate due to an end impact. On the example of numerical calculations, the invariance of the elastic force and energy characteristics of the medium during solid-state rotations is confirmed.