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Scaling laws for implicit viscosities in smoothed particle hydrodynamics

: Bierwisch, C.; Polfer, P.

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Radjai, F. ; Association for the Study of Micromechanics of Granular Media:
Powders and Grains 2017. 8th International Conference on Micromechanics on Granular Media : Montpellier, France, July 3-7, 2017
Les Ulis: EDP Sciences, 2017 (EPJ Web of Conferences 140)
Art. 15008, 4 pp.
International Conference on Micromechanics on Granular Media <8, 2017, Montpellier>
Conference Paper, Electronic Publication
Fraunhofer IWM ()
SPH; periodic fluidic system; viscosity

Smoothed particle hydrodynamics (SPH) is a particle-based method which solves continuum equations such as the Navier-Stokes equations. A periodic fluidic system under homogeneous shear is studied using SPH in the present work. The total pressure of the system and the shear stress contributions from the SPH interaction terms for pressure and viscosity as well as the contribution caused by velocity fluctuations are analyzed. It is found that the pressure and the shear stress contributions obey certain scaling laws depending on physical properties of the system such as compressibility, viscosity and shear rate as well as the spatial resolution. Some of the identified relations resemble scaling laws for the rheology of dense granular flows. These findings render an assessment of the convergence with respect to the spatial resolution of SPH simulations possible. Furthermore, the similarities between numerical SPH particles and physical grains in dense flow provide a deeper understanding of the nature of the SPH method.