, Volume 49, Issue 9, pp 2153–2167 | Cite as

Slender-body theory for viscous flow via dimensional reduction and hyperviscous regularization

New Trends in Fluid and Solid Mechanical Models


A new slender-body theory for viscous flow, based on the concepts of dimensional reduction and hyperviscous regularization, is presented. The geometry of flat, elongated, or point-like rigid bodies immersed in a viscous fluid is approximated by lower-dimensional objects, and a hyperviscous term is added to the flow equation. The hyperviscosity is given by the product of the ordinary viscosity with the square of a length that is shown to play the role of effective thickness of any lower-dimensional object. Explicit solutions of simple problems illustrate how the proposed method is able to represent with good approximation both the velocity field and the drag forces generated by rigid motions of the immersed bodies, in analogy with classical slender-body theories. This approach has the potential to open up the way to more effective computational techniques, since geometrical complexities can be significantly reduced. This, however, is achieved at the expense of involving higher-order derivatives of the velocity field. Importantly, both the dimensional reduction and the hyperviscous regularization, combined with suitable numerical schemes, can be used also in situations where inertia is not negligible.


Slender-body theory Hyperviscosity Fluid-structure interaction Dimensional reduction 

Mathematics Subject Classification (2000)

76D07 76A05 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Fisica “N. Tartaglia”Università Cattolica del Sacro CuoreBresciaItaly
  2. 2.Mathematical Soft Matter UnitOkinawa Institute of Technology Graduate UniversityKunigami-gunJapan

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