Commun. Comput. Phys., 12 (2012), pp. 1257-1274.


Computational Aspects of Multiscale Simulation with the Lumped Particle Framework

Omar al-Khayat 1*, Hans Petter Langtangen 2

1 Computational Geosciences, CBC, Simula Research Laboratory, P.O. Box 134, NO-1325 Lysaker, Norway.
2 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 11 February 2011; Accepted (in revised version) 12 December 2011
Available online 17 April 2012
doi:10.4208/cicp.110211.121211a

Abstract

First introduced in [2], the lumped particle framework is a flexible and numerically efficient framework for the modelling of particle transport in fluid flow. In this paper, the framework is expanded to simulate multicomponent particle-laden fluid flow. This is accomplished by introducing simulation protocols to model particles over a wide range of length and time scales. Consequently, we present a time ordering scheme and an approximate approach for accelerating the computation of evolution of different particle constituents with large differences in physical scales. We apply the extended framework on the temporal evolution of three particle constituents in sand-laden flow, and horizontal release of spherical particles. Furthermore, we evaluate the numerical error of the lumped particle model. In this context, we discuss the Velocity-Verlet numerical scheme, and show how to apply this to solving Newton's equations within the framework. We show that the increased accuracy of the Velocity-Verlet scheme is not lost when applied to the lumped particle framework.

AMS subject classifications: 65L12, 65L70, 68W25, 86-08, 34E13, 34E99

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Key words: Multiscale modelling, lumped particle model, Velocity-Verlet scheme.

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

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