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An accurate method to include lubrication forces in numerical simulations of dense Stokesian suspensions

Published online by Cambridge University Press:  25 March 2015

A. Lefebvre-Lepot ,
B. Merlet  and
T. N. Nguyen
A. Lefebvre-Lepot
Affiliation:
CNRS – Ecole Polytechnique/CMAP, route de Saclay, 91128 Palaiseau CEDEX, France
B. Merlet*
Affiliation:
Ecole Polytechnique/CMAP, route de Saclay, 91128 Palaiseau CEDEX, France
T. N. Nguyen
Affiliation:
Ecole Polytechnique/CMAP, route de Saclay, 91128 Palaiseau CEDEX, France
*
†Email address for correspondence: benoit.merlet@cmap.polytechnique.fr
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Abstract

We address the problem of computing the hydrodynamic forces and torques among $N$ solid spherical particles moving with given rotational and translational velocities in Stokes flow. We consider the original fluid–particle model without introducing new hypotheses or models. Our method includes the singular lubrication interactions which may occur when some particles come close to one another. The main new feature is that short-range interactions are propagated to the whole flow, including accurately the many-body lubrication interactions. The method builds on a pre-existing fluid solver and is flexible with respect to the choice of this solver. The error is the error generated by the fluid solver when computing non-singular flows (i.e. with negligible short-range interactions). Therefore, only a small number of degrees of freedom are required and we obtain very accurate simulations within a reasonable computational cost. Our method is closely related to a method proposed by Sangani & Mo (Phys. Fluids, vol. 6, 1994, pp. 1653–1662) but, in contrast with the latter, it does not require parameter tuning. We compare our method with the Stokesian dynamics of Durlofsky et al. (J. Fluid Mech., vol. 180, 1987, pp. 21–49) and show the higher accuracy of the former (both by analysis and by numerical experiments).

JFM classification

Low-Reynolds-number flows: Boundary integral methods Low-Reynolds-number flows: Lubrication theory Low-Reynolds-number flows: Stokesian dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 769 , 25 April 2015 , pp. 369 - 386
Copyright
© 2015 Cambridge University Press 

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