Commun. Comput. Phys., 8 (2010), pp. 115-142.


A Lumped Particle Modeling Framework for Simulating Particle Transport in Fluids

Omar al-Khayat 1*, Are Magnus Bruaset 2, Hans Petter Langtangen 3

1 Computational Geosciences, CBC, Simula Research Laboratory, P.O. Box 134, NO-1325 Lysaker, Norway.
2 Computational Geosciences, CBC, Simula Research Laboratory, P.O. Box 134, NO-1325 Lysaker, Norway; and Department of Informatics, University of Oslo, P.O. Box 1080, Blindern, NO-0316 Oslo, Norway.
3 Department of Informatics, University of Oslo, P.O. Box 1080, Blindern, NO-0316 Oslo, Norway; and Center for Biomedical Computing, Simula Research Laboratory, P.O. Box 134, NO-1325 Lysaker, Norway.

Received 3 May 2009; Accepted (in revised version) 14 October 2009
Available online 12 February 2010
doi:10.4208/cicp.030509.141009a

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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PACS: 47.55.Kf, 47.57.Gc
Key words: Particle modeling framework, particle transport, lumped particle model.

*Corresponding author.
Email: omark@simula.no (O. al-Khayat), arem@simula.no (A. M. Bruaset), hpl@simula.no (H. P. Langtangen)
 

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