The Derivation and Application of Fundamental Solutions for Unsteady Stokes Equations

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 presented, based on the vector calculus method and also the Hörmander’s method. The mathematical derivation pr...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mechanics 2015-12, Vol.31 (6), p.683-691
Main Authors: Hsiao, C-H., Young, D.-L.
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Derivation
Fluid flow
Mathematical analysis
Mechanics
Navier-Stokes equations
Stokes flow
Stokes law (fluid mechanics)
Studies
Three dimensional
Unsteady
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 presented, based on the vector calculus method and also the Hörmander’s method. The mathematical derivation process for the fundamental solutions is detailed. The steady fundamental solutions of Stokes equations can be obtained from the unsteady fundamental solutions by the integral process. As an application, we adopt fundamental solutions: an unsteady Stokeslet and an unsteady potential dipole to validate a simple case that a sphere translates in Stokes or low-Reynolds-number flow by using the singularity method instead by the traditional method which in general limits to the assumption of oscillating flow. It is concluded that this study is able to extend the unsteady Stokes flow theory to more general transient motions by making use of the fundamental solutions of the linearly unsteady Stokes equations.
ISSN:1727-7191
1811-8216
DOI:10.1017/jmech.2015.70