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

Giulio G. Giusteri; Alfredo Marzocchi; Alessandro Musesti

doi:10.3934/dcdsb.2014.19.2145

Article Contents

2014, Volume 19, Issue 7: 2145-2157. Doi: 10.3934/dcdsb.2014.19.2145

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

1.
Dipartimento di Matematica e Fisica "N. Tartaglia", Università Cattolica del Sacro Cuore, Via dei Musei 41, I-25121 Brescia

Received: April 30, 2013

Revised: February 28, 2014

Published: August 2014

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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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Mathematics Subject Classification: Primary: 76D03; Secondary: 35Q35.

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