Formulation and Stability Analysis of a Multi-Scale Modeling Approach for Simulation of Elastic Wave Propagation

Abstract

In this work, we report on the formulation and detailed stability analysis of a dynamic multi-scale scheme involving two different local computational strategies for modeling of elastic wave propagation. The coupled model involves the Local Interaction Simulation Approach and Cellular Automata for Elastodynamics, however the presented analysis approach is general and applies to other numerical techniques. This scheme is capable of coupling two numerical models with possibly dissimilar spatial discretization lengths and material properties, hence it is appealing for a multi-scale and/or multi-resolution analysis. The method developed in this paper employs an interface force–displacement coupling to yield the multi-scale model equations. It is shown that the governing equations contain a self-coupling term that affects the stability of the system, as it contributes to additional stiffness at the interface. Stability analysis is presented in terms of rotations of two vectors in [Formula: see text] space, where each vector represents individual model’s stability. Three model configurations of practical interest were investigated, analytical formulae derived and used to analyze stability. These analytical formulae were compared against results from numerical simulations and perfect agreement was observed.