Modeling the behavior of complex media by jointly using discrete and continuum approaches

We propose a new approach to modeling the behavior of heterogeneous media, according to which such objects are represented as composed of regions of two types, one being described within the framework of a discrete, and the other, a continuum approach. This joint approach is promising for the numerical modeling of complex media with strongly different properties of components. Possibilities of the proposed method were verified by studying the propagation of elastic waves in a two-component medium with a discrete component, modeled by the method of movable cellular automata, and a continuum component described by a system of equations of motion of continuum solved by the finite difference method. The results of calculations show that this approach provides adequate description of the propagation of elastic waves in complex media and does not introduce nonphysical distortions at the boundaries where the two models are matched.