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

Giulio Giuseppe Giusteri, Eliot Fried

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

4 Citazioni (Scopus)

Abstract

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.
Lingua originaleEnglish
pagine (da-a)N/A-N/A
RivistaMeccanica
Volume2014
DOI
Stato di pubblicazionePubblicato - 2014

Keywords

  • Dimensional reduction
  • Fluid-structure interaction
  • Hyperviscosity
  • Slender-body theory

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