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arXiv · 1305.1180

Nonlinear free fall of one-dimensional rigid bodies in hyperviscous fluids

Giulio G. Giusteri·Alfredo Marzocchi·Alessandro Musesti
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Abstract

We consider the free fall of slender rigid bodies in a viscous incompressible fluid. We show that the dimensional reduction (DR), performed by substituting the slender bodies with one-dimensional rigid objects, together with a hyperviscous regularization (HR) of the Navier--Stokes equation for the three-dimensional fluid lead to a well-posed fluid-structure interaction problem. In contrast to what can be achieved within a classical framework, the hyperviscous term permits a sound definition of the viscous force acting on the one-dimensional immersed body. Those results show that the DR/HR procedure can be effectively employed for the mathematical modeling of the free fall problem in the slender-body limit.

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Giulio G. Giusteri, Alfredo Marzocchi, Alessandro Musesti. 2013-05-06. Nonlinear free fall of one-dimensional rigid bodies in hyperviscous fluids. https://doi.org/10.3934/dcdsb.2014.19.2145

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