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A new slender-body theory for viscous flow, based on the concepts ofdimensional reduction and hyperviscous regularization, is presented. Thegeometry of flat, elongated, or point-like rigid bodies immersed in a viscousfluid is approximated by lower-dimensional objects, and a hyperviscous term isadded to the flow equation. The hyperviscosity is given by the product of theordinary viscosity with the square of a length that is shown to play the roleof effective thickness of any lower-dimensional object. Explicit solutions ofsimple problems illustrate how the proposed method is able to represent withgood approximation both the velocity field and the drag forces generated byrigid motions of the immersed bodies, in analogy with classical slender-bodytheories. This approach has the potential to open up the way to more effectivecomputational techniques, since the complexity of the geometry can besignificantly reduced. This, however, is achieved at the expense of involvinghigher-order derivatives of the velocity field. Importantly, both thedimensional reduction and the hyperviscous regularization, combined withsuitable numerical schemes, can be used also in situations where inertia is notnegligible.

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