2001
DOI: 10.1103/physreve.63.051201
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Generalized fundamental solutions for unsteady viscous flows

Abstract: A number of closed-form fundamental solutions for 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 forces acting on a sphere and on a circular cylinder translating in an unsteady rotating flow field at low Reynolds numbers are calculated using the generalized fundament… Show more

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Cited by 18 publications
(15 citation statements)
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References 23 publications
(16 reference statements)
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“…Efforts also have been made to solve unsteady Stokes flows by the singularity method [25,35,36] and inverse two-dimensional Stokes problems [37]. The MFS has also been applied to Brinkman flow including the case of Brinkman flow with Robin BC at the interface with another fluid [38].…”
Section: Introductionmentioning
confidence: 99%
“…Efforts also have been made to solve unsteady Stokes flows by the singularity method [25,35,36] and inverse two-dimensional Stokes problems [37]. The MFS has also been applied to Brinkman flow including the case of Brinkman flow with Robin BC at the interface with another fluid [38].…”
Section: Introductionmentioning
confidence: 99%
“…domains, or the so-called Stokeslet and Oseenlet, have been extensively examined [1,[4][5][6][7]. Recently, Venkatalaxmi et al [6] showed that the solution for an unsteady Stokeslet can be expressed in a general form that involves two scalar functions.…”
mentioning
confidence: 98%
“…Recently, Venkatalaxmi et al [6] showed that the solution for an unsteady Stokeslet can be expressed in a general form that involves two scalar functions. Shu and Chwang [7] derived analytical solutions for the generalized unsteady Stokeslet and Oseenlet.…”
mentioning
confidence: 99%
“…Price and Tan [15] provided a convolution-integral formulation for a transient Oseenlet. Chan and Chwang [10] and Shu and Chwang [11] derived a series of generalized 3D unsteady Oseenlets.…”
mentioning
confidence: 99%