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arXiv · 1403.3247

Generalized fundamental solutions for unsteady viscous flows

Jian-Jun Shu·Allen T. Chwang
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Abstract

A number of new closed-form fundamental solutions for the generalized unsteady Oseen and Stokes flows associated with arbitrary time-dependent translational and rotational motions have been developed. These solutions are decomposed into two parts corresponding to a longitudinal wave and a transversal wave. As examples of application, the hydrodynamic force acting on a sphere or on a circular cylinder translating in an unsteady flow field at low Reynolds numbers are calculated using the new generalized fundamental solutions. The results for a rotating viscous flow past an impulsively moving sphere and an impulsively moving circular cylinder are entirely new.

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Jian-Jun Shu, Allen T. Chwang. 2014-03-13. Generalized fundamental solutions for unsteady viscous flows. https://doi.org/10.1103/physreve.63.051201

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