An Approach for Solving Three-Dimensional Fluid Dynamics Problems with Allowance for Elastic Processes

A finite-difference approximation of elastic forces on Lagrangian grids is constructed by applying the support operator method. For displacement vectors on unstructured grids with minimal reasonable constraints imposed on their topological and geometric structure, approximations of vector analysis operations are constructed as applied to difference schemes for elasticity problems. Taking into account the energy balance of the medium, the constructed families of integrally consistent approximations of vector analysis operations are sufficient for discrete simulation of these processes. Schemes are considered in which the stress tensor is used in explicit form or is split into a spherical and a shear component (pressure and deviator). The latter approach is used to construct uniform algorithms applicable to both the solid body and the evaporated phase. The approximations are constructed using linear elasticity theory. The resulting forces are obtained in explicit form in three-dimensional geometry. Sound waves propagating in a three-dimensional orthogonal aluminum plate as generated by an impact on its end are computed.