A Lumped Particle Modeling Framework for Simulating Particle Transport in Fluids

Abstract

This paper presents a lumped particle model for simulating a large number of particles. The lumped particle model is a flexible framework in modeling particle flows, embodying fundamental features that are intrinsic in particle laden flow, including advection, diffusion and dispersion. In this paper, the particles obey a simplified version of the Bassinet-Boussinesq-Oseen equation for a single spherical particle. However, instead of tracking the individual dynamics of each particle, a weighted spatial averaging procedure is used where the external forces are applied to a "lump" of particles, from which an average position and velocity is derived. The temporal evolution of the particles is computed by partitioning the lumped particle into smaller entities, which are then transported throughout the physical domain. These smaller entities recombine into new particle lumps at their target destinations. For particles prone to the effects of Brownian motion or similar phenomena, a symmetric spreading of the particles is included as well. Numerical experiments show that the lumped particle model reproduces the effects of Brownian diffusion and uniform particle transport by a fluid and gravity. The late time scale diffusive nature of particle motion is also reproduced.

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