A numerical method for fully resolved simulation (FRS) of rigid particle–flow interactions in complex flows

A fictitious-domain based formulation for fully resolved simulations of arbitrary shaped, freely moving rigid particles in unsteady flows is presented. The entire fluid–particle domain is assumed to be an incompressible, but variable density, fluid. The numerical method is based on a finite-volume approach on a co-located, Cartesian grid together with a fractional step method for variable density, low-Mach number flows. The flow inside the fluid region is constrained to be divergence-free for an incompressible fluid, whereas the flow inside the particle domain is constrained to undergo rigid body motion. In this approach, the rigid body motion constraint is imposed by avoiding the explicit calculation of distributed Lagrange multipliers and is based upon the formulation developed by Patankar [N. Patankar, A formulation for fast computations of rigid particulate flows, Center for Turbulence Research Annual Research Briefs 2001 (2001) 185–196]. The rigidity constraint is imposed and the rigid body motion (translation and rotational velocity fields) is obtained directly in the context of a two-stage fractional step scheme. The numerical approach is applied to both imposed particle motion and fluid–particle interaction problems involving freely moving particles. Grid and time-step convergence studies are performed to evaluate the accuracy of the approach. Finally, simulation of rigid particles in a decaying isotropic turbulent flow is performed to study the feasibility of simulations of particle-laden turbulent flows.