Generalized fundamental solutions for unsteady viscous flows
Fluid Dynamics
2014-03-14 v1
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.
Cite
@article{arxiv.1403.3247,
title = {Generalized fundamental solutions for unsteady viscous flows},
author = {Jian-Jun Shu and Allen T. Chwang},
journal= {arXiv preprint arXiv:1403.3247},
year = {2014}
}