A Monolithic Framework for the Simulation of Free-Surface Non-Newtonian Fluid Flow with Multiple Immersed Solids

Resumo

This work presents a monolithic computational framework for simulating free-surface incompressible non-Newtonian flows with multiple immersed solid bodies. The methodology combines a particle-position-based formulation of the Particle Finite Element Method (PFEM) for the fluid phase and a total Lagrangian finite element formulation for the solid phase. Both fluid and solid models use nodal positions as primary variables. This unified treatment enables direct and consistent coupling between fluid and solid domains. Interactions between immersed solids are handled through a node-to-surface contact formulation enforced via Lagrange multipliers. The fluid is described by the Bingham–Papanastasiou constitutive model, while the solid is described by the Saint-Venant–Kirchhoff constitutive model. For temporal discretization, the implicit Generalized-α time-marching scheme is adopted, offering second-order accuracy and enhanced stability through controlled numerical dissipation of high-frequency effects. The proposed methodology demonstrates strong potential for applications such as simulating concrete flow, where the mortar is treated as a non-Newtonian fluid and the coarse aggregates as immersed solid particles.