Hybrid Modeling of Elastic Wave Propagation: Domain Coupling and Stability

This paper reports on a formulation and analysis of a coupling scheme for elastic wave propagation modeling. Two local computational strategies are considered, namely, the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE). While LISA can work only with rectangular cells, CAFE is capable of simulating waves in both triangular and rectangular lattices. Thus, a hybrid approach is of great interest since the non-uniform mesh capability of CAFE triangular cells can be readily coupled to LISA’s rectangular grids, taking advantage of the built-in LISA features on the uniform portion of the domain. This paper provides an insight into the formulation of LISA and CAFE and dynamic coupling of these techniques. The idea of the hybrid approach involves coupling of an overlapping interface between LISA and CAFE domains with a self-coupling process, wherein elastic and inertial forces are coupled dynamically. The self-coupling property of the hybrid scheme results in a non-obvious stability criterion for the explicit time integration scheme used for wave propagation. The coupling is analyzed analytically, so close-form expressions are found for finding the critical time step for the coupled model. Next, the coupled model is tested for different ratios of cell discretization lengths in LISA and CAFE, and the stability is analyzed for different ratios.