Bridging coupled discrete-continuum multi-scale approach for dynamic analysis

A novel multi-scale method coupling continuum-based and discrete-based approaches is proposed in this study, which effectively eliminates spurious wave reflections without necessitating any additional filtering or damping. It starts with the discretization of the entire domain into two distinct elements: meshes for the finite difference method (FDM) and particles for the discrete element method (DEM). Lagrange multipliers are introduced so that compatibility of dynamic behavior between the DEM-based and FDM-based models is enforced. The dynamic governing equations are derived for the multi-scale subdomains using the energy potential function. Based on the central difference method, a multi-scale dynamic explicit algorithm is proposed to solve the established multi-scale dynamic coupling system. This multi-scale method couples two existing commercial packages: the DEM-based code PFC, and the FDM-based code FLAC. The new method is applied to several referencing cases. Good results are obtained from the proposed method when compared with the numerical results obtained from FDM and DEM.