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Semi-implicit operator splitting for the simulation of Herschel–Bulkley flows with smoothed particle hydrodynamics

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Abstract

Smoothed particle hydrodynamics (SPH) has become a popular numerical framework of choice for simulating free-surface flows, mainly for Newtonian fluids. The topic regarding the simulation of non-Newtonian free-surface flows, however, remains relatively untouched due to difficulties regarding the computation of viscous forces. In previous approaches, the viscous forces acting on each SPH particle were computed explicitly. Non-Newtonian fluids such as Herschel–Bulkley fluids, the effective viscosity between yielded and unyielded regions can differ by several orders of magnitudes; imposing severe time step restrictions for the simulation for explicit methods. Numerically, this can be seen as a stiff problem. We propose a semi-implicit time-stepping approach where the viscous forces are computed implicitly, within the context of SPH. We demonstrate the convergence of the method via a simple 2D test case.

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Acknowledgements

The research was not funded by any third party organization.

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  1. University of California, Berkeley, Etcheverry Hall, Berkeley, CA, 94720-1740, USA

    Chang Yoon Park & Tarek I. Zohdi

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  1. Chang Yoon Park
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  2. Tarek I. Zohdi
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Correspondence to Chang Yoon Park.

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Park, C.Y., Zohdi, T.I. Semi-implicit operator splitting for the simulation of Herschel–Bulkley flows with smoothed particle hydrodynamics. Comp. Part. Mech. 7, 699–704 (2020). https://doi.org/10.1007/s40571-019-00301-9

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  • DOI: https://doi.org/10.1007/s40571-019-00301-9

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