Numerical simulation of shock-wave processes in elastic media and structures. Part I: Solving method and algorithms

Finite-difference algorithms for solving non-stationary wave problems are presented, which allow to obtain the description of fronts and front zones with a minimal influence of spurious effects of numerical approximation. The principal condition of the construction of calculation algorithms is the convergence of domains of dependence of continual and difference equations. It is shown that the fulfillment of this condition provides a maximally exact wave fronts description. Numerical solutions of several one-dimensional and two-dimensional wave problems are presented. In the second part of the paper, we will give examples of numerical simulation of applied problems of structure dynamics and geodynamics - impact driving of piles into the soil, formation of pendulum waves in a block massif, stress state of a homogeneous massif in the zone of interaction with a punch, fracture of a layered solid under the action of a local pulse, and high-speed penetration of a layered target.