A Monolithic Lattice Boltzmann–Fictitious Domain Method for Particle Sedimentation

• Extension of the fictitious domain approach to the Lattice Boltzmann method. • No explicit computation of hydrodynamic forces and no transfer to a solid solver. • The method enforces rigid-body constraints in the solid domain through a newly introduced source term that modifies viscous effects at the macroscopic level in the LBM framework. • The LBM-ID2Q9 formulation is employed to extend the fluid equations in the solid domain. • The proposed method has been successfully applied to various cases of particle sedimentation. A monolithic fictitious domain method is introduced within the Lattice Boltzmann (LBM) framework to model fluid–structure interactions involving rigid bodies, with application to particle sedimentation. The proposed approach unifies the fluid and solid domains within a single set of evolution equations. Rigid-body motion is enforced by modifying the collision operator inside the solid region: a source term acting on the second-order moment of the distribution function drives the strain-rate tensor toward zero, so that the rigid velocity emerges directly from the LBM dynamics without prescribing a target velocity or invoking a separate solid solver. This formulation eliminates the need for force computations, thereby extending the fictitious domain concept to the LBM in a truly monolithic fashion. The method preserves the inherent simplicity and locality of the LBM algorithm and is naturally well-suited for large-scale parallel computations. Numerical experiments demonstrate that the approach accurately reproduces rigid-body motion and complex hydrodynamic interactions, from simple sedimentation cases to dense suspensions involving a large number of interacting particles.