A variational formulation based contact algorithm for rigid boundaries in two-dimensional SPH applications

Smooth particle Hydrodynamics (SPH) is one of the most effective meshless techniques used in computational mechanics. SPH approximations are simple and allow greater flexibility in various engineering applications. However, modelling of particle-boundary interactions in SPH computations has always been considered an aspect that requires further research. A number of techniques have been developed to model particle-boundary interactions in SPH and allied methods. In this paper, an innovative approach is introduced to handle the contact between Lagrangian SPH particles and rigid solid boundaries. The formulation of boundary contact forces are derived based on a variational formulation, thus directly ensuring the conservativeness of the governing equations. In addition, the new elegant boundary contact force terms maintain the simplicity of the SPH governing equations.