Slender body theory for Stokes flows with regularized forces. (English) Zbl 1452.76055

Cortez, Ricardo; Nicholas, Michael

Commun. Appl. Math. Comput. Sci. 7, No. 1, 33-62 (2012).

Summary: Existing slender body theories for the dynamics of a thin tube in a Stokes flow differ in the way the asymptotic errors depend on a small parameter defined as the radius of the body over its length. Examples are the theory of Lighthill, that of Keller and Rubinow, and that of Johnson. Slender body theory is revisited here in the more general setting of forces which are localized but smoothly varying within a small neighborhood of the filament centerline, rather than delta distributions along the centerline. Physically, this means that the forces are smoothly distributed over the cross-section of the body. The regularity in the forces produces a final expression that has built-in smoothing which helps eliminate instabilities encountered in computations with unsmoothed formulas. Consistency with standard theories is verified in the limit as the smoothing parameter vanishes, where the original expressions are recovered. In addition, an expression for the fluid velocity at locations off the slender body is derived and used to compute the flow around a filament.

MSC:

76D07	Stokes and related (Oseen, etc.) flows
76Z10	Biopropulsion in water and in air
76M45	Asymptotic methods, singular perturbations applied to problems in fluid mechanics

Keywords:

slender body theory; Stokes flow