Implicit Hybrid Grid-Characteristic Method for Modeling Dynamic Processes in Acoustic Medium

The paper discusses the process of developing an implicit second-order grid-characteristic method taking into account conditions at the boundary, as well as its monotonization using an implicit first-order method and a grid-characteristic monotonicity criterion. We obtained analytical expressions for the values at the boundary nodes at the next time layer for boundary conditions of constant force or constant velocity and the considered schemes. The approach obtained is applied to simulate dynamic processes in isotropic linear elastic medium. In model formulations, both acoustic waves with a high propagation velocity and macro waves with a low propagation velocity were observed.