An Impulse-Based Collision Approach for Rigid Bodies with Arbitrary Shape in the Phase-Field Model
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In the field of Fluid–Structure Interactions (FSI), the contact between solid bodies and boundaries represents a highly relevant research topic. Such problems arise in a wide range of applications, from microorganism motion in biophysics to sediment transport in geoscience and particle–fluid interaction in lubrication systems. The Phase-Field Method (PFM), originally developed for phase transitions in materials science [1], has increasingly been extended to multiphase flow and FSI problems owing to its natural capability of handling interfacial phenomena. By implicitly representing interfaces and consistently incorporating interfacial thermodynamics, PFM provides a flexible framework for problems involving complex topology. This work focuses on a simplified yet practical setting where solid bodies are assumed rigid, neglecting deformations during contact. This assumption is justified for applications involving stiff particles like sand or stones, which can be treated as undeformable within the flow. Unlike existing PFM-based approaches emphasizing deformable bodies [2], this study concentrates on a physically consistent description of collision dynamics. An impulse-based collision model [3] is adopted for a diffuse representation of rigid bodies within a flow. The framework ensures physically consistent behavior, particularly regarding momentum exchange and energy consistency for rigid bodies in incompressible fluids. The collision model is validated in vacuum to assess collision behavior under dry conditions. Further adaptations ensure compatibility with diffuse interfaces. Benchmark problems are evaluated against analytical solutions to investigate accuracy and convergence. Numerical results demonstrate convergent collision behavior, reliable momentum transfer, and robust performance in demanding interaction scenarios. The model is then tested with classic FSI benchmarks to further validate the feasibility of the PFM fluid solver and the collision model.
