# Generalized fundamental solutions for unsteady viscous flows.

@article{Shu2001GeneralizedFS, title={Generalized fundamental solutions for unsteady viscous flows.}, author={Jian-Jun Shu and Allen T. Chwang}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2001}, volume={63 5 Pt 1}, pages={ 051201 } }

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…

## 26 Citations

The Derivation and Application of Fundamental Solutions for Unsteady Stokes Equations

- Mathematics, Engineering
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In this paper, two formulations in explicit form to derive the fundamental solutions for two and three dimensional unsteady unbounded Stokes flows due to a mass source and a point force are…

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The equations for the hydrodynamic force and torque acting on a sphere in unsteady Stokes equations under different flow conditions are solved analytically by means of the singularity method. This…

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New fundamental solutions for micropolar fluids are derived in explicit form for two- and three-dimensional steady unbounded Stokes and Oseen flows due to a point force and a point couple, including…

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- 2011

New fundamental solutions for micropolar fluids have been obtained in explicit form by considering Stokes and Oseen flows due to a point force and a point couple. Fundamental solutions that do not…

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The interaction of unsteady Stokeslets with the free surface of an initially quiescent incompressible fluid of infinite depth is investigated analytically for two- and three-dimensional cases. The…

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- 2014

General solution representations for velocity and pressure fields describing transient flows at small Reynolds numbers (Stokes flows) and flows obeying Brinkman models are presented. The geometry…

Transient Marangoni Waves Due to Impulsive Motion of a Submerged Body

- Physics, Engineering
- 2004

The Oseen problem in a viscous fluid is formulated for studying the transient free-surface and Marangoni waves generated by the impulsive motion of a submerged body beneath a surface with…

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The interfacial capillary–gravity waves due to a transient fundamental singularity immersed in a system of two semi-infinite immiscible fluids of different densities are investigated analytically for…

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The interfacial capillary–gravity waves due to a transient fundamental singularity immersed in a system of two semi-infinite immiscible fluids of different densities are investigated analytically for…

Method of fundamental solutions for partial‐slip fibrous filtration flows

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In this study a Stokeslet‐based method of fundamental solutions (MFS) for two‐dimensional low Reynolds number partial‐slip flows has been developed. First, the flow past an infinitely long cylinder…

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