Lagrangian numerical simulation of particulate flows

The Lagrangian numerical simulation (LNS) scheme presented in this paper is motivated by the multiphase particle-in-cell (MP-PIC). In this numerical scheme we solve the fluid phase continuity and momentum equations on an Eulerian grid. The particle motion is governed by Newton's law thus following the Lagrangian approach. Momentum exchange from the particle to fluid is modeled in the fluid phase momentum equation. Forces acting on the particle include drag from the fluid, body force and force due to interparticle stress. There is freedom to use different models for these forces and to introduce other forces. The effect of viscous stresses are included in the fluid phase equations. The volume fraction of the particles appear in the fluid phase continuity and momentum equations. A finite volume method is used to solve for the fluid phase equations on an Eulerian grid. Particle positions are updated using the Runge-Kutta scheme. This numerical scheme can handle a range of particle loadings and particle types. The LNS scheme is implemented using an efficient three-dimensional time dependent finite volume algorithm. We use a Chorin-type pressure-correction based fractional-step scheme on a non-staggered cartesian grid. In this paper, we consider only incompressible Newtonian suspending fluid. However, the average velocity field of the fluid phase is not divergence-free because its effective density is not constant. Our pressure correction based fractional-step scheme accounts for varying properties in the fluid phase equations. This method can also account for suspending fluids with non-constant properties. The numerical scheme is verified by comparing results with test cases and experiments.